We investigate the constancy of the Le numbers of one parameter deformations F :(C X Cn, 0) — (C, 0) of holomorphic germs of functions f :(Cn, 0) — (C, 0) which have singular set with any dimension s > 1. WecharacterizeLe constant deformations in terms of the non-splitting of the polar varieties and also from the integral closure of the ideal Jz (F) in On+1 generated by the partial derivatives of F with respect to the variables z = (z!,...,zn)