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A nonuniform version of the Berry-Esseen bound has been proved. The mostimportant feature of the new bound is a monotonically decreasing functionC(|t|) instead of the universal constant C=29.1174: C(|t|)<C if |t| > 3.2, andC(|t|) tends to 1+e if |t| is increasing.  The function C(|t|) has very complex analytical expression based on indicatorfunctions. A general algorithm was developed in order to estimate values ofC(|t|) for an arbitrary t.

An Algorithm to Estimate a Nonuniform Convergence Bound in the Central Limit Theorem