The multivariate normal probability of a given rectangular region as a function of correlations is approximated by TAYLOR polynomials. Because of the poor convergence properties of the classical tetrachoric expansion the center of this series is shifted to a correlation matrix Romnear the given matrix R, where Ro has a simple m-factirial structure. For computiations only m≦2 is used. For the convergence of this expansion a sufficient condition is proved. Especially for the distribution of the maximum modulus satisfying results are obtained for larger probabilities using only TALYLOR polynomials of 2nd degree with m=1