Problem with QR method for Hessenberg matrices

In trying to implement the method, my approach is to use a reduction to Hessenberg form, and then to iterate using a QR method of Givens rotations. However, I am having trouble successfully implementing the Givens rotations, since I'm only worried about the n−1 entries of the off-diagonal, in a manner of speaking. Included is my MATLAB code:

function [H,Q,R] = hessQR(A,maxIter)
[H,P] = HHhess(A);
for k = 1:maxIter
   [Q,R] = HGivQR(H);
   A = R*Q;
end
end

function [Q,R] = HGivQR(A)
n = size(A,1);
Q=eye(n);
R=A;
for j=1:n-1    
  for i=n:(-1):j+1        
      x=R(:,j);   
      if norm([x(i-1),x(i)])>0       
          c=x(i-1)/norm([x(i-1),x(i)]);
          s=-x(i)/norm([x(i-1),x(i)]);
          G=eye(n);
          G([i-1,i],[i-1,i])=[c,s;-s,c];
          R=G'*R;
          Q=Q*G;
      end
  end
end
end

The method converges, but my real Schur decomposition (which is R in my code) is not correct... nor is A==Q*R. I'm not sure what I'm doing wrong, but I think it might be in my Givens code. Please, point out mistakes you see that I have made!