Let ${gij (x)}^n_i,j=1$ and ${L_ij (x)}^n_i,j=1$ be the sets of all coefficients of the first and second fundamental forms of a hypersurface x in Rn+1 . For a connected open subset U ⊂ $R^n$ and a C∞ -mapping x : U → $R^{n+1}$ the hypersurface x is said to be d -nondegenerate, where d ∈ {1, 2, . . . n} , if Ldd(x) ̸ = 0 for all u ∈ U . Let M (n) = {F : $R_n$ −→ $R_n$ | F x = gx + b, g ∈ O(n), b ∈ Rn} , where O(n) is the group of all real orthogonal n × n -matrices, and SM (n) = {F ∈ M (n) | g ∈ SO(n)} , where SO(n) = {g ∈ O(n) | det(g) = 1} . In the present paper, it is proved that the set ${g_ij$ (x), $L_dj$ (x), i, j = 1, 2, . . . , n} is a complete system of a SM (n + 1) -invariants of a d -non-degenerate hypersurface in $R^{n+1}$ . A similar result has obtained for the group M (n + 1) .