  In the study of the algebra $\mathrm{NCSym}$ of symmetric functions in
noncommutative variables, Bergeron and Zabrocki found a free generating set
consisting of power sum symmetric functions indexed by atomic partitions. On
the other hand, Bergeron, Reutenauer, Rosas, and Zabrocki studied another free
generating set of $\mathrm{NCSym}$ consisting of monomial symmetric functions
indexed by unsplitable partitions. Can and Sagan raised the question of finding
a bijection between atomic partitions and unsplitable partitions. In this
paper, we provide such a bijection.
