We report a measurement of the streaming motion of the stars in the Galactic bar with the red clump giants (RCGs) using the data of the Optical Gravitational Lensing Experiment II (OGLE-II). We measure the proper motion of 46961 stars and divide RCGs into bright and faint subsamples that on average will be closer to the near and far sides of the bar, respectively. We find that the far-side RCGs (4979 stars) have a proper motion of {Delta}<{mu}>~1.5+/-0.11mas/yr toward the negative longitudes relative to the near-side RCGs (3610 stars).