There is a kind of non-Doppler redshift, the theory of redshift shows a new redshift mechanism, in which the redshift is proportional to distances between the galaxies. This principle of redshift arises from both of the running inertia deviated from the local equivalence principle at cosmological distances and the De Broglie's basic equation related the wavelength to the momentum of elementary particle. According to this principle, the Hubble's law could be explained without Doppler redshift. This is a kind of steady state redshift and performs a large-scale nonlinear effect, which has nothing to do with the hypotheses of cosmic expansion and accelerated expansion. The cosmological redshift formula is
Z = ln(1+HD/C),
where, Z is redshift determination; H is Hubble constant; C is velocity of light, D is redshift distance.
This cosmological redshift formula would not only describe the universe beyond the boundary of Hubble's Law, but also evolve back to Hubble's Law in low-redshift scale.
By this method, using the theory and formula of cosmological redshift as the validation technique in determining distances to high-redshift supernovae, the results of 43 high-redshift (Z = 0.172 - 1.755) type Ia supernovae show that the redshift distances determined by the cosmological redshift formula and the Luminosity distance have a good match within the measurement uncertainties.