>> x = mvnrnd(zeros(1,2),C1,10000);
>> y = mvnrnd(zeros(1,2),C2,10000);
>> chol(cov([x y]))

ans =

   1.006891868834764   0.503933797681249   0.020078812622287   0.020822623330906
                   0   0.858042430837816  -0.003546103543455   0.000418070006100
                   0                   0   1.009117616854190   0.804374268640588
                   0                   0                   0   0.596874185204538

>> chol(cov(x))

ans =

   1.006891868834764   0.503933797681249
                   0   0.858042430837815

>> chol(cov(y))

ans =

   1.009323584492180   0.804622886594552
                   0   0.596902440778913