  In this paper, we introduce the concept of completely positive matrix of
linear maps on Hilbert $A$-modules over locally $C^{*}$-algebras and prove an
analogue of Stinespring theorem for it. We show that any two minimal
Stinespring representations for such matrices are unitarily equivalent.
Finally, we prove an analogue of the Radon--Nikodym theorem for this type of
completely positive $n\times n$ matrices.
