Let the mean and variance of W be 0 and 1 respectively.The zero-biased dis tribution.of W is defined to be the distribution of W* which satisfies the equation EWf(W) =Ef(W*) for all bounded functions f with bounded derivatives f.Using tlis equation and Steins method, one can easily obtain a simple error bound on the total variation distance between the distribution of W* and N(0,1).We use this result to study discretized normal approximation for sums of integer-valued random variables.