  Recently Leggett's proposal of non-local model generates new interest in
simulating the statistics of singlet state. Singlet state statistics can be
simulated by 1 bit of classical communication without using any further
nonlocal correlation. But, interestingly, singlet state statistics can also be
simulated with no classical cost if a non-local box is used. In the first case,
the output is completely unbiased whereas in second case outputs are completely
random. We suggest a new (possibly) signaling correlation resource which
successfully simulates singlet statistics and this result suggests a new
complementary relation between required classical bits and randomness in local
output when the classical communication is limited by 1 cbit. This result
reproduces the above two models of simulation as extreme cases. This also
explains why Leggett's non-local model and the model presented by Branciard
et.al. should fail to reproduce the statistics of a singlet.
