There is presently available a large number of techniques purporting to accomplish the inversion of matrices. While the purely mathematical aspects of this problem, on one hand, are thus well recognized, the computational ones, on the other hand, are not. The growth of the rounding error, in particular, may be so rapid as to make some inversion procedures altogether unstable. It is from this point of view that the partitioning method seems to be capable of yielding more accurate results than do other methods. By stopping, at any desired step, to improve the intermediate inverses until satisfactory accuracy is attained, the growth of the rounding error may be kept in check.