diff --git a/matlab/disp_dr.m b/matlab/disp_dr.m
index 9e5deeab0..ab7208e83 100644
--- a/matlab/disp_dr.m
+++ b/matlab/disp_dr.m
@@ -1,3 +1,4 @@
+
 function disp_dr(dr,order,var_list)
 % Display the decision rules
 %
@@ -102,11 +103,7 @@ end
 %
 for k=1:nx
     flag = 0;
-    if options_.block
-        str1 = subst_auxvar(dr.state_var(k),-1);
-    else
-        str1 = subst_auxvar(k1(klag(k,1)),klag(k,2)-M_.maximum_lag-2);
-    end;
+    str1 = subst_auxvar(dr.state_var(k),-1);
     str = sprintf('%-20s',str1);
     for i=1:nvar
         x = dr.ghx(ivar(i),k);
diff --git a/matlab/dyn_first_order_solver.m b/matlab/dyn_first_order_solver.m
index 86b5fb31b..988be3ffc 100644
--- a/matlab/dyn_first_order_solver.m
+++ b/matlab/dyn_first_order_solver.m
@@ -1,7 +1,7 @@
-function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
-    
+function [dr,info] = dyn_first_order_solver(jacobia,DynareModel,dr,DynareOptions,task)
+
 %@info:
-%! @deftypefn {Function File} {[@var{dr},@var{info}] =} dyn_first_order_solver (@var{jacobia},@var{M_},@var{dr},@var{options},@var{task})
+%! @deftypefn {Function File} {[@var{dr},@var{info}] =} dyn_first_order_solver (@var{jacobia},@var{DynareModel},@var{dr},@var{DynareOptions},@var{task})
 %! @anchor{dyn_first_order_solver}
 %! @sp 1
 %! Computes the first order reduced form of the DSGE model
@@ -11,7 +11,7 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
 %! @table @ @var
 %! @item jacobia
 %! Matrix containing the Jacobian of the model
-%! @item M_
+%! @item DynareModel
 %! Matlab's structure describing the model (initialized by @code{dynare}).
 %! @item dr
 %! Matlab's structure describing the reduced form solution of the model.
@@ -41,7 +41,7 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
 %! @item info==5
 %! Blanchard & Kahn conditions are not satisfied: indeterminacy due to rank failure.
 %! @item info==7
-%! One of the generalized eigenvalues is close to 0/0     
+%! One of the generalized eigenvalues is close to 0/0
 %! @end table
 %! @end table
 %! @end deftypefn
@@ -63,75 +63,107 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
 %
 % You should have received a copy of the GNU General Public License
 % along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
-    
-    info = 0;
-    
-    dr.ghx = [];
-    dr.ghu = [];
-    
-    klen = M_.maximum_endo_lag+M_.maximum_endo_lead+1;
-    kstate = dr.kstate;
-    kad = dr.kad;
-    kae = dr.kae;
-    nstatic = dr.nstatic;
-    nfwrd = dr.nfwrd;
-    npred = dr.npred;
-    nboth = dr.nboth;
+
+persistent reorder_jacobian_columns innovations_idx index_s index_m index_c index_p row_indx index_0m index_0p k1 k2 j3 j4
+persistent ndynamic nstatic nfwrd npred nboth nd nyf n
+
+
+if ~nargin
+    reorder_jacobian_columns = [];
+    dr = [];
+    info = [];
+    return
+end
+
+if isempty(reorder_jacobian_columns)
+
+    kstate   = dr.kstate;
+    nfwrd    = dr.nfwrd;
+    nboth    = dr.nboth;
+    npred    = dr.npred-nboth;
+    nstatic  = dr.nstatic;
+    ndynamic = npred+nfwrd+nboth;
+    nyf      = nfwrd + nboth;
+    n        = ndynamic+nstatic;
+
+    k1 = 1:(npred+nboth);
+    k2 = 1:(nfwrd+nboth);
+
     order_var = dr.order_var;
     nd = size(kstate,1);
-    lead_lag_incidence = M_.lead_lag_incidence;
+    lead_lag_incidence = DynareModel.lead_lag_incidence;
     nz = nnz(lead_lag_incidence);
 
-    sdyn = M_.endo_nbr - nstatic;
+    %lead variables actually present in the model
+    j4 = nstatic+npred+1:nstatic+npred+nboth+nfwrd;   % Index on the forward and both variables
+    j3 = nonzeros(lead_lag_incidence(2,j4)) - nstatic - 2 * npred - nboth;  % Index on the non-zeros forward and both variables
+    j4 = find(lead_lag_incidence(2,j4));
 
-    [junk,cols_b,cols_j] = find(lead_lag_incidence(M_.maximum_endo_lag+1,...
-                                                   order_var));
-    
-    if nstatic > 0
-        [Q,R] = qr(jacobia(:,cols_j(1:nstatic)));
-        aa = Q'*jacobia;
-    else
-        aa = jacobia;
-    end
-    k1 = find([1:klen] ~= M_.maximum_endo_lag+1);
-    a = aa(:,nonzeros(lead_lag_incidence(k1,:)'));
-    b(:,cols_b) = aa(:,cols_j);
-    b10 = b(1:nstatic,1:nstatic);
-    b11 = b(1:nstatic,nstatic+1:end);
-    b2 = b(nstatic+1:end,nstatic+1:end);
-    if any(isinf(a(:)))
-        info = 1;
-        return
+    no_lead_id = find(lead_lag_incidence(3,:)==0);
+    no_lag_id = find(lead_lag_incidence(1,:)==0);
+
+    static_id = intersect(no_lead_id,no_lag_id);
+    lag_id = setdiff(no_lead_id,static_id);
+    lead_id = setdiff(no_lag_id,static_id);
+    both_id = intersect(setdiff(1:n,no_lead_id),setdiff(1:n,no_lag_id));
+
+    lead_idx = lead_lag_incidence(3,lead_id);
+    lag_idx = lead_lag_incidence(1,lag_id);
+    both_lagged_idx = lead_lag_incidence(1,both_id);
+    both_leaded_idx = lead_lag_incidence(3,both_id);
+    innovations_idx = (size(jacobia,2)-DynareModel.exo_nbr+1):size(jacobia,2);
+    dr.state_var  = [lag_idx, both_lagged_idx];
+
+    indexi_0 = 0;
+    if DynareModel.maximum_endo_lag > 0 && (npred > 0  || nboth > 0)
+        indexi_0 = min(lead_lag_incidence(2,:));
     end
 
-    % buildind D and E
-    d = zeros(nd,nd) ;
-    e = d ;
+    index_c  = lead_lag_incidence(2,:);             % Index of all endogenous variables present at time=t
+    index_s  = lead_lag_incidence(2,1:nstatic);     % Index of all static endogenous variables present at time=t
+    index_0m = (nstatic+1:nstatic+npred)+indexi_0-1;
+    index_0p = (nstatic+npred+1:n)+indexi_0-1;
+    index_m  = 1:(npred+nboth);
+    index_p  = lead_lag_incidence(3,find(lead_lag_incidence(3,:)));
+    row_indx = nstatic+1:n;
 
-    k = find(kstate(:,2) >= M_.maximum_endo_lag+2 & kstate(:,3));
-    d(1:sdyn,k) = a(nstatic+1:end,kstate(k,3)) ;
-    k1 = find(kstate(:,2) == M_.maximum_endo_lag+2);
-    e(1:sdyn,k1) =  -b2(:,kstate(k1,1)-nstatic);
-    k = find(kstate(:,2) <= M_.maximum_endo_lag+1 & kstate(:,4));
-    e(1:sdyn,k) = -a(nstatic+1:end,kstate(k,4)) ;
-    k2 = find(kstate(:,2) == M_.maximum_endo_lag+1);
-    k2 = k2(~ismember(kstate(k2,1),kstate(k1,1)));
-    d(1:sdyn,k2) = b2(:,kstate(k2,1)-nstatic);
+    reorder_jacobian_columns = [lag_idx, both_lagged_idx, npred+nboth+[static_id lag_id both_id lead_id], both_leaded_idx, lead_idx, innovations_idx ];
 
-    if ~isempty(kad)
-        for j = 1:size(kad,1)
-            d(sdyn+j,kad(j)) = 1 ;
-            e(sdyn+j,kae(j)) = 1 ;
-        end
-    end
+end
 
-    % 1) if mjdgges.dll (or .mexw32 or ....) doesn't exit, 
-    % matlab/qz is added to the path. There exists now qz/mjdgges.m that 
-    % contains the calls to the old Sims code 
-    % 2) In  global_initialization.m, if mjdgges.m is visible exist(...)==2, 
-    % this means that the DLL isn't avaiable and use_qzdiv is set to 1
-    
-    [err,ss,tt,w,sdim,dr.eigval,info1] = mjdgges(e,d,options.qz_criterium);
+info = 0;
+
+dr.ghx = [];
+dr.ghu = [];
+
+jacobia = jacobia(:,reorder_jacobian_columns);
+
+if nstatic > 0
+    [Q, junk] = qr(jacobia(:,index_s));
+    aa = Q'*jacobia;
+else
+    aa = jacobia;
+end
+
+A = aa(:,index_m);  % Jacobain matrix for lagged endogeneous variables
+B = aa(:,index_c);  % Jacobian matrix for contemporaneous endogeneous variables
+C = aa(:,index_p);  % Jacobain matrix for led endogeneous variables
+
+if task ~= 1 && DynareOptions.dr_cycle_reduction == 1
+    A1 = [aa(row_indx,index_m ) zeros(ndynamic,nfwrd)];
+    B1 = [aa(row_indx,index_0m) aa(row_indx,index_0p) ];
+    C1 = [zeros(ndynamic,npred) aa(row_indx,index_p)];
+    [ghx, info] = cycle_reduction(A1, B1, C1, DynareOptions.dr_cycle_reduction_tol);
+    ghx = ghx(:,index_m);
+    hx = ghx(1:npred+nboth,:);
+    gx = ghx(1+npred:end,:);
+end
+
+if (task ~= 1 && ((DynareOptions.dr_cycle_reduction == 1 && info ==1) || DynareOptions.dr_cycle_reduction == 0)) || task == 1
+    D = [[aa(row_indx,index_0m) zeros(ndynamic,nboth) aa(row_indx,index_p)] ; [zeros(nboth, npred) eye(nboth) zeros(nboth, nboth + nfwrd)]];
+    E = [-aa(row_indx,[index_m index_0p])  ; [zeros(nboth,nboth+npred) eye(nboth,nboth+nfwrd) ] ];
+
+    [err, ss, tt, w, sdim, dr.eigval, info1] = mjdgges(E,D,DynareOptions.qz_criterium);
     mexErrCheck('mjdgges', err);
 
     if info1
@@ -141,21 +173,19 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
         else
             info(1) = 2;
             info(2) = info1;
-            info(3) = size(e,2);
+            info(3) = size(E,2);
         end
         return
     end
 
     nba = nd-sdim;
 
-    nyf = sum(kstate(:,2) > M_.maximum_endo_lag+1);
-
     if task == 1
         dr.rank = rank(w(1:nyf,nd-nyf+1:end));
         % Under Octave, eig(A,B) doesn't exist, and
         % lambda = qz(A,B) won't return infinite eigenvalues
         if ~exist('OCTAVE_VERSION')
-            dr.eigval = eig(e,d);
+            dr.eigval = eig(E,D);
         end
         return
     end
@@ -163,74 +193,86 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
     if nba ~= nyf
         temp = sort(abs(dr.eigval));
         if nba > nyf
-            temp = temp(nd-nba+1:nd-nyf)-1-options.qz_criterium;
+            temp = temp(nd-nba+1:nd-nyf)-1-DynareOptions.qz_criterium;
             info(1) = 3;
         elseif nba < nyf;
-            temp = temp(nd-nyf+1:nd-nba)-1-options.qz_criterium;
+            temp = temp(nd-nyf+1:nd-nba)-1-DynareOptions.qz_criterium;
             info(1) = 4;
         end
         info(2) = temp'*temp;
         return
     end
 
-    np = nd - nyf;
-    n2 = np + 1;
-    n3 = nyf;
-    n4 = n3 + 1;
-    % derivatives with respect to dynamic state variables
-    % forward variables
-    w1 =w(1:n3,n2:nd);
-    if ~isscalar(w1) && (condest(w1) > 1e9);
-        % condest() fails on a scalar under Octave
-        info(1) = 5;
-        info(2) = condest(w1);
-        return;
-    else
-        gx = -w1'\w(n4:nd,n2:nd)';
-    end  
-
-    % predetermined variables
-    hx = w(1:n3,1:np)'*gx+w(n4:nd,1:np)';
-    hx = (tt(1:np,1:np)*hx)\(ss(1:np,1:np)*hx);
-
-    k1 = find(kstate(n4:nd,2) == M_.maximum_endo_lag+1);
-    k2 = find(kstate(1:n3,2) == M_.maximum_endo_lag+2);
-    dr.gx = gx;
-    dr.ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
-
-    %lead variables actually present in the model
-    j3 = nonzeros(kstate(:,3));
-    j4  = find(kstate(:,3));
-    % derivatives with respect to exogenous variables
-    if M_.exo_nbr
-        fu = aa(:,nz+(1:M_.exo_nbr));
-        a1 = b;
-        aa1 = [];
-        if nstatic > 0
-            aa1 = a1(:,1:nstatic);
+    %First order approximation
+    if task ~= 1
+        indx_stable_root = 1: (nd - nyf);     %=> index of stable roots
+        indx_explosive_root = npred + nboth + 1:nd;  %=> index of explosive roots
+                                                     % derivatives with respect to dynamic state variables
+                                                     % forward variables
+        Z = w';
+        Z11t = Z(indx_stable_root,    indx_stable_root)';
+        Z21  = Z(indx_explosive_root, indx_stable_root);
+        Z22  = Z(indx_explosive_root, indx_explosive_root);
+        if ~isfloat(Z21) && (condest(Z21) > 1e9)
+            info(1) = 5;
+            info(2) = condest(Z21);
+            return;
+        else
+            gx = - Z22 \ Z21;
         end
-        dr.ghu = -[aa1 a(:,j3)*gx(j4,1:npred)+a1(:,nstatic+1:nstatic+ ...
-                                                 npred) a1(:,nstatic+npred+1:end)]\fu;
+        % predetermined variables
+        hx =  Z11t * inv(tt(indx_stable_root, indx_stable_root)) * ss(indx_stable_root, indx_stable_root) * inv(Z11t);
+        ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
+    end;
+end
+
+if  task~= 1
+
+    if nstatic > 0
+        B_static = B(:,1:nstatic);  % submatrix containing the derivatives w.r. to static variables
     else
-        dr.ghu = [];
-    end
+        B_static = [];
+    end;
+    %static variables, backward variable, mixed variables and forward variables
+    B_pred = B(:,nstatic+1:nstatic+npred+nboth);
+    B_fyd = B(:,nstatic+npred+nboth+1:end);
 
     % static variables
     if nstatic > 0
-        temp = -a(1:nstatic,j3)*gx(j4,:)*hx;
-        j5 = find(kstate(n4:nd,4));
-        temp(:,j5) = temp(:,j5)-a(1:nstatic,nonzeros(kstate(:,4)));
-        temp = b10\(temp-b11*dr.ghx);
-        dr.ghx = [temp; dr.ghx];
+        temp = - C(1:nstatic,j3)*gx(j4,:)*hx;
+        b = aa(:,index_c);
+        b10 = b(1:nstatic, 1:nstatic);
+        b11 = b(1:nstatic, nstatic+1:n);
+        temp(:,index_m) = temp(:,index_m)-A(1:nstatic,:);
+        temp = b10\(temp-b11*ghx);
+        ghx = [temp; ghx];
         temp = [];
     end
 
-    if options.use_qzdiv
-        %% Necessary when using Sims' routines for QZ
-        gx = real(gx);
-        hx = real(hx);
-        dr.ghx = real(dr.ghx);
-        dr.ghu = real(dr.ghu);
-    end
+    A_ = real([B_static C(:,j3)*gx+B_pred B_fyd]); % The state_variable of the block are located at [B_pred B_both]
 
-    dr.Gy = hx;
\ No newline at end of file
+    if DynareModel.exo_nbr
+        if nstatic > 0
+            fu = Q' * jacobia(:,innovations_idx);
+        else
+            fu = jacobia(:,innovations_idx);
+        end;
+
+        ghu = - A_ \ fu;
+    else
+        ghu = [];
+    end;
+end
+
+
+dr.ghx = ghx;
+dr.ghu = ghu;
+
+if DynareOptions.aim_solver ~= 1 && DynareOptions.use_qzdiv
+    % Necessary when using Sims' routines for QZ
+    dr.ghx = real(ghx);
+    dr.ghu = real(ghu);
+    hx = real(hx);
+end
+
+dr.Gy = hx;
\ No newline at end of file