A=[-1,-1,0,0;-1,1,0,0;1,-1,0,0;1,1,0,0];
# eigs with
#
# if (rows (a) < 4) # instead of if (rows (a) < 9)
#   call_eig = true;
# endif
[V,s] = eigs([sparse(4,4),A;A',sparse(4,4)],4,4);
# I see that V(1:4,3)'*V(1:4,4) is not zero
u = [sqrt(2)*V(1:4,1:2),orth(V(1:4,3:4))];
v = [sqrt(2)*V(5:8,1:2),orth(V(5:8,3:4))];
u'*u # is orthogonal
v'*v # is orthogonal
u*s*v # is A
