  The Galactic bulge shows a double red clump in sight lines with |b| > 5 deg
and -3 deg < l < 4 deg. 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 deg we find that the
proper motion difference between the two arms is a linear function of the
Galactic longitude for -0.1 deg < l < 0.5 deg, 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 deg < l < -0.1 deg, which gives us an estimate of bulge
rotation speed of 87.9 +/- 8.2 km/s/kpc.
