Let G be the group M(n) generated by all orthogonal transformations and translations of the n-dimensional Euclidean space or G be the subgroup of M(n) generated by rotations and translations of . This paper presents the conditions of G-equivalence for two B,zier curves in of degree m, where . Moreover, two minimal complete systems of control G-invariants of a B,zier curve are obtained. The definition of a non-directional B,zier curve is introduced and a complete system of control G-invariants of this curve is obtained. Correlations between elements of the second minimal complete system of control M(n)-invariants are investigated.