  The Mullineux involution is a relevant map that appears in the study of the
modular representations of the symmetric group and the alternating group. The
fixed points of this map are certain partitions of particular interest. It is
known that the cardinality of the set of these self-Mullineux partitions is
equal to the cardinality of a distinguished subset of self-conjugate
partitions. In this work, we give an explicit bijection between the two
families of partitions in terms of the Mullineux symbol.
