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It will be very important of polarization as contrast mechanism and a characterization of the optical polarization properties of a turbid medium, such as a biological tissue. Because birefringence is one of the relative phenomena of polarization, we analyzed the propagation of polarized light in a linearly birefringent turbid medium and simulated all two- dimensional elements of diffusely backscattered Muller matrix of the medium using the Stocks Mueller formalism and Monte Carlo algorithm. Some of the elements present unusual spatial patterns compared with those for a non-birefringent isotropic turbid medium. Statistical distributions of the changes of polarization in the turbid medium with different birefringent parameters are demonstrated.