The main result in this paper is an extension of T. D. Zhong's for the boundary properties of a Bochner-Martinelli type integral on a bounded domain withC2-smooth boundary and on a manifold withC2-smooth boundary to a Stein manifold with piecewise smooth boundaries (even to non-closed piecewise smooth Stein manifold). Using the local expression of the Henkin-Leiterer kernel in term of usual Bochner-Martinelli type kernel defined on Stein manifolds, the author proves a more general Plemelj formula:are both belong toH(vbD) for the Bochner-Martinelli transform on piecewise smooth manifolds.