Phase averaged velocity fields in the near wake region behind a square cylinder have been (successfully) obtained using randomly sampled PIV data sets. The Reynolds number based on the flow velocity and the vertex height was 3,900. To identify the phase information, we examined the magnitude of circulation and the center of peak vorticity. The center of vorticity was estimated from lowpass filtered vorticity contours (LES decomposition) adopting a sub-pixel searching algirithm. Due to the sinusoidal nature of firculation which is closely related to the instantaneous vorticity, the location of peak voticity fits well with a sine curve of the circulation magnitude. Conditionally-averaged velocity fields represent the barman vortex shedding phenomenon very well within 5 degrees phase uncertainty. The oscillating nature of the separated shear layer and the separation bubble at the top surface are clearly observed. With the hot-wire measurements of Strouhal frequency, we found thats the convection velocity changes its magnitude very rapidly from 25 to 75 percent of the free stream velocity along the streamwise direction when the flow passes by the recirculation region.