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Magnetic properties of the low-doped high-T c cuprates are studied, based on the numerical diagonalization of the finite cluster t-J model. We show the pseudogap behavior observed in the temperature dependence of the NMR relaxation rate, the neutron scattering intensity and the magnetic susceptibility, etc. associated with the presence of the antiferromagnetic spin correlation. The effect of the next-nearest neighbor hopping t' is also presented.