Abstract: Blind channel order estimation is a key technique for deterministic blind channel identification based on second order statistics; many blind channel order estimation methods are useless under ill-conditioned channel environment. In subspace method, when channel order is correct and over determined, the special toeplitz matrix constituted by the noise vectors is singular, the radio of maximum and minimum singular value is infinity. This paper employs the maximum and minimum singular value ratio of the special matrix to establish an extreme eigenvalues theorem (MMR theorem). Considering the finite and noisy observation samples, this paper proposes a new channel order estimation algorithm (MMRR algorithm) based on MMR theorem; the goal function of the MMRR algorithm uses extreme eigenvalues ratio according to different order values, this function can get the global maximum at the correct and/or effective channel order. Finally, this paper employs typical channel parameters(well-conditioned channel and ill-conditioned channel) for simulation and analysis, under the finite samples and moderate SNRs, the simulation results show that this method can correctly estimate effective order of well-conditioned and ill-conditioned channels with high probability, which outperforms other existing algorithms.