  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 $\mathcal{P}$ of $E$ into $k$
common independent sets, where the difference of the cardinalities of any two
sets in $\mathcal{P}$ is at most one.
