Summary: The spectrum of discrete Schrödinger operator \(L+V\) on the \(d\)-dimensional lattice is considered, where \(L\) denotes the discrete Laplacian and \(V\) a delta function with mass at a single point. Eigenvalues of \(L+V\) are specified and the absence of singular continuous spectrum is proven. In particular it is shown that an embedded eigenvalue does appear for \(d\geq 5\) but does not for \(1\leq d\leq 4\).