The present note is a strengthening of a recent paper by K. Takazawa and Y. Yokoi (A generalized-polymatroid approach to disjoint common independent sets in two matroids, Discrete Mathematics (2019)). For given two matroids on E , under the same assumption in their paper to guarantee the existence of a partition of E into k common independent sets of the two matroids, we show that there exists a nearly uniform partition P of E into k common independent sets, where the difference of the cardinalities of any two sets in P is at most one.