It will be assumed that the reader is familiar w,ith the elementary theory of congruences [1]. Let in, M2, ... *, mn be s integers relatively prime in pairs and let Ml =MIM2 im8. Let xl, x2, * * , x8be an ordered set of s integers such that 0 < xi < mi. There exists one and only one residue class x mod 31 such that x xi (mod mi) andwethereforewritex=(xl,x2," , X8).Ifx= (xl, ,x8),y= (y1,* ,Y.) then x y = (x1 i Yy, * * , x8 4 y), xy = (x1y1, , x.y8), where the ith coordinates must be reduced mod mi. The symbols (xi, * , x,) are called modular numbers, but it should be kept in mind that (xi, * , x,) does not denote a number but a residue class mod Ml. The purpose of this note is to describe a simple iterative procedure to determine the least non-negative residue mod Mll of a given residue class (xl, * * *, x,). The iteration process described below gives the least non-negative residue in mixed radix representation. Notation. The moduli are denoted by mi, m *, in8. We put mo = 1,