As there exists an inconsistency in claiming the symmetrical relations in the 16 Mueller matrix elements used to describe a turbid medium, the author restudies the symmetrical relationships between diffusely backscattered polarization patterns in isotropic turbid media and simulates all two-dimensional elements of diffusely backscattered Mueller matrix in both cases of Rayleigh and Mie scatterings using the double-scattering approximation and the Monte Carlo algorithm, respectively. The previous experimental observations are compared with the numerically determined matrix elements, showing a good agreement in both double-scattering model and Monte Carlo simulation. The symmetrical relations between the Mueller matrix elements are clarified.