  Suppose $T$ and $S$ are bounded adjointable operators between Hilbert
C*-modules admitting bounded Moore-Penrose inverse operators. Some necessary
and sufficient conditions are given for the reverse order law $(TS)^{ \dag}
=S^{ \dag} T^{ \dag}$ to hold. In particular, we show that the equality holds
if and only if $Ran(T^{\ast}TS) \subseteq Ran(S)$ and $Ran(SS^{\ast}T^{\ast})
\subseteq Ran(T^{\ast}),$ which was studied first by Greville [{\it SIAM Rev. 8
(1966) 518--521}] for matrices.
