  In this paper, we discuss the invariant properties of curvatures effected by
the Matsumoto's $C$ or $L$-process. We find equivalent conditions on curvatures
by comparing the difference between the corresponding curvatures of closely
related connections. As an application, Matsumoto's $L$-process on Randers
manifold is studied. Shen connection can not be obtained by using Matsumoto's
processes from other well-known connections. This leads us to two new processes
which we call Shen's $C$ and $L$-processes. We study the invariant properties
of curvatures under the Shen's processes.
