The orthonormal basis of a system of shifts of one trigonometric polynomial exist in the space of complex trigonometric polynomials with components from m to n and in the space of real trigonometric polynomials with components from 0 to n. Under condition 0 < m < n there is no orthogonal basis of shifts of one trigonometric polynomial in this space real trigonometric polynomials with components from m to n. The system of shifts of two trigonometric polynomials are orthogonal basis in this space.
