The starting point lies in the results obtained by Sedov (1944) for isotropic turbulence with a self-preserving hypothesis.A careful consideration of the mathematical structure of the Kaxman-Howaxth equation leads to an exact analysis of all cases possible and to all admissible solutions of the problem.I study this interesting problem from a new point of view.New solutions axe obtained.Based on these exact solutions, some physical significant consequences of recent advances in the theory of self-preserved homogeneous statistical solution of the Navier-Stokes equations axe presented.