Let M be a differential manifold endowed with a Riemannian almost product structure (f,g). A CH-change of g is defined by the author and H. T. Hopteriev in [C. R. Acad. Bulg. Sci. 37, 473-475 (1984; Zbl 0548.53019)]. The present paper deals with the study of CH-invariants and to the manifolds CH-equivalent to a locally decomposable manifold. Some classes of the classification given by A. M. Naveira [Rend. Mat. Appl., VII. Ser. 3, 577-592 (1983; Zbl 0538.53045)] are proved here to be CH-invariant.