  In 1992, Agache and Chaple introduced the concept of a semi-symmetric
non-metric connection([1]). The semi-symmetric non-metric connection does not
satisfy the Schur`s theorem. The purpose of the present paper is to study some
properties of a new semi-symmetric non-metric connection satisfying the Schur`s
theorem in a Riemannian manifold. And we considered necessary and sufficient
condition that a Riemannian manifold with a semi-symmetric non-metric
connection be a Riemannian manifold with constant curvature.
