Turbulent flow characteristics in the near wake of a square cylinder have been studied experimentally by using a Digital PIV method. Experiments are performed at the Reynolds numbers of 1600 and 3900 based on the free-stream velocity and the square height. The ensemble averaged turbulence statistics are acquired from 2030 realizations of instantaneous fluctuating velocity field after the conventional Reynolds decomposition. The differences in turbulent intensity and Reynolds shear stress profiles fur both oases indicate that the effect of Reynolds number seems to be descernible mainly due to the occurrence of transition in the separated shear layer. Because of the periodic nature of vortex shedding process, transverse velocity fluctuations contribute dominantly , to turbulent kinetic energy distribution. A comparison with previous LDV data obtained at much higher Reynolds number shows a fairly good agreement each other. It turns out that the effect of Reynolds number diminishes as increasing Reynolds number, which is a well-known feature of a sharp-edged bluff body wake. The streamwise variation of turbulence intensities are compared with those from a circular cylinder along the centerline at the same Reynolds number. The overall magnitudes and the decay rates of turbulence intensities are quite similar, but some differences are noticeble especially in the transverse intensity variation.