  Many theorems and formulas of Lie algebras run quite parallel to Lie
superalgebra case, sometimes giving interesting results. So it is quite natural
to extend the new concepts of Lie algebra immediately to Lie superalgebra case,
as these type of algebras have wide applications in physics and related
theories. Using the concept of isoclinism, F. Saeedi and S. Sheikh-Mohseni
recently studied the central derivation of nilpotent Lie algebra with nilindex
2. The purpose of the present paper is to continue and extend the investigation
to obtain some similar results for Lie superalgebras, as isoclinism in Lie
superalgebra is being recently introduced.
