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This paper introduces a multi-keyhole model for designing MIMO radio-relay systems which can realize a multi-stream transmission to an isolated area. Probability density function (PDF) of eigenvalues of channel correlation matrix in the multi-keyhole environment is highlighted. We derive an approximated formula for the probability density function of all eigenvalues connecting to a space diversity approximation. It is shown that the calculated values based on the proposed method agree very well with the simulated values.