Let P be a fixed probability measure and suppose that (2=QI* ' "*Qk is close to P. Then there exists a decomposition P=P~*'"*Pk such that Pj is close to Qj for each j. This stability property holds fairly generally, and when valid, it is easily established by compactness arguments [1]. The property plays an essential role in the limit theorems for sums of independent random variables that are not necessarily infinitesimal [11]. Several authors have given estimates for the rate of stability in particular cases, such as for normal [9, 4, 10], Poisson [8], and binomial [7] distributions. In the present paper, the corresponding problem is treated for arbitrary finitely supported probability measures in free modules.