The authors prove that for any graded metric on a graded manifold there exists a unique torsionless and metric graded connection. The formula used to define the metric graded connection coincides with the one given by the reviewer for even metrics on supermanifolds [cf. the reviewer, Preprint, Seminarul de Mecanica, Univ. Timisoara 30 (1990)]. Starting from a Riemannian metric \(g\), the authors also define an odd metric \(G\) and study the gradient, divergence and Laplacian operators for \(G\).