The convergence of any iterative method discribed by x^k+1 = A(x^k), where A is an algorythm operating Euclid or Hilbert space and x^k, x^k+1 are iterations of the method, can be improved by exact relaxation one knows an estimation of the type ||A(x)-α||x - α ||, where α is an immovable point of the algorythm, constant c ≤ I. To construct the next iteration the modifical algorythm of type x^k + y(A(x,^k) - X^k) is proposed. The current iteration x ^k, its image A(x^k), the current evaluation d ≥ || x^k-α || are used to calculate the optimal γ and the next evaluation of ||x^k+1 - α||. A tool for the construction is the attainability domain of the attendant differential game. The expances to calculate the optimal relaxation is very modest in comparison with ones of symplicst base algorythms.