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The physical conjecture about the crossover for $N\times N$ 1DÌýrandomÌýband matrices with the band width $W$ states that we get the same behavior of eigenvalues correlation functions as forÌýGUEÌýfor $W\gg \sqrt{N}$ (which corresponds toÌýdelocalizedÌýstates), and we get another behavior, which is determined by theÌýPoissonÌýstatistics, for $W\ll \sqrt{n}$ (and corresponds to localized states). The question is still open (there are some partial results only), however, the first part of the conjecture was proved for more accessible objects than eigenvalues correlation functions, namely, for the correlation functions of characteristic polynomials. In this talk we complement this result and prove that for $W\ll \sqrt{n}$ the behavior of the second correlation function of characteristic polynomials is different from those for $GUE$. ÌýJoint work with Mariya Shcherbina.Ìý