  The universal central extensions and their extension kernels of the matrix
Lie superalgebra sl(m, n, A), the Steinberg Lie superalgebra st(m, n, A) in
category {\bf SLeib} of Leibniz superalgebras are determined under a weak
assumption (compared with \cite{MP}) using the first Hochschild homology and
the first cyclic homology group.
