We give an elementary proof of the sharp Bernstein type inequality(Formula presented.). Here n, r, s ∈ ℕ, f is a 2π-periodic spline of order r and of minimal defect with nodes jπ/n, j ∈ Z, δ_h ^sis the difference operator of order s with step h, and the K_mare the Favard constants. A similar inequality for the space L₂(ℝ) is also established. Bibliography: 5 titles.