  We study the graded derivation-based noncommutative differential geometry of
the $Z_2$-graded algebra ${\bf M}(n| m)$ of complex $(n+m)\times(n+m)$-matrices
with the ``usual block matrix grading'' (for $n\neq m$). Beside the
(infinite-dimensional) algebra of graded forms the graded Cartan calculus,
graded symplectic structure, graded vector bundles, graded connections and
curvature are introduced and investigated. In particular we prove the
universality of the graded derivation-based first-order differential calculus
and show, that ${\bf M}(n|m)$ is a ``noncommutative graded manifold'' in a
stricter sense: There is a natural body map and the cohomologies of ${\bf
M}(n|m)$ and its body coincide (as in the case of ordinary graded manifolds).
