Abstract: In the present note we have considered Mn to be a Riemannian manifold admitting a semi-symmetric recurrent metric connection. The aim of the present paper is to obtain the conditions under which the quasi-conformal curvature tensor and M-projective curvature tensor of semi-symmetric recurrent metric connection and the Riemannian connection to be equal.Key words: Semi-symmetric recurrent metric connection, quasi-conformal curvature tensor, M-projective curvature tensor.In the present note we have considered recurrent metric connection. The aim of the present paper is to obtain the conditions under which the quasiconformal curvature tensor and -projective curvature tensor of semi-symmetric recurrent metric connection and the Riemannian connection to be equal.  to be a Riemannian manifold admitting a semi-symmetric