minimize a function with matrix output subject to a constrain

Dear all, I have another question about minimizing a function using Matlab. I already post a question here: Minimizing Function With Matrix Output and the result is as what I expected, matrix output. But the value is still incorrect. I forgot that the function has a constrain. Here is my code:

function f=obj1(C,H12,H21,F1,F2)
f=norm(H12*F2-C(:,1)*C(:,1)'*H12*F2)^2+norm(H21*F1-C(:,2)*C(:,2)'*H21*F1)^2;

Here is how I call the function:

find_C = @(T) obj1(T, H(:,:,1,2), H(:,:,2,1), F(:,:,1), F(:,:,2));
guess=rand(3,2);
Cout = fminsearch(find_C, guess,options);
C(:,:,1)=Cout(:,1);
C(:,:,2)=Cout(:,2);

H12 and H21 are 3x3 matrix, F1 and F2 are 3x1 matrix. I want to minimize the function to find C(:,1) and C(:,2) and it should be a 3x1 matrix, with constrain C(:,2)*C(:,2)'=I and C(:,1)*C(:,1)'=I (identity matrix).

I read about fmincon, but I thought the constrain is different. Do you have any idea to solve this?

Thank you!