The Galactic bulge shows a double red clump in sight lines with |b| \gtrsim 5 ^ { \circ } and -3 ^ { \circ } \lesssim l \lesssim 4 ^ { \circ } .
It is interpreted as a signature of an X -shaped structure seen almost edge-on .
We measure the proper motions of the stars belonging to the closer and the further arm of the X -shaped structure .
The intrinsic kinematic properties of the two arms are found by incorporating information taken from the luminosity function .
At b = -5 ^ { \circ } we find that the proper motion difference between the two arms is a linear function of the Galactic longitude for -0.1 ^ { \circ } < l < 0.5 ^ { \circ } , which we interpret as a streaming motion of the stars within the X -shaped structure .
Such a streaming motion has not previously been reported .
The proper motion difference is constant for -0.8 ^ { \circ } < l < -0.1 ^ { \circ } , which gives us an estimate of bulge rotation speed of 87.9 \pm 8.2 ~ { } { km~ { } s ^ { -1 } ~ { } kpc ^ { -1 } } .