  We derive accurate proper motions of the CH3OH 12 GHz masers towards the
W3(OH) UCHII region, employing seven epochs of VLBA observations spanning a
time interval of about 10 yr. The achieved velocity accuracy is of the order of
0.1 km/s, adequate to precisely measure the relative velocities of most of the
12 GHz masers in W3(OH), with amplitude varying in the range 0.3 - 3 km/s.
Towards W3(OH), the most intense 12 GHz masers concentrate in a small area
towards the north (the northern clump) of the UCHII region. We have compared
the proper motions of the CH3OH 12 GHz masers with those (derived from
literature data) of the OH 6035 MHz masers, emitting from the same region of
the methanol masers. In the northern clump, the two maser emissions emerge from
nearby (but likely distinct) cloudlets of masing gas with, in general, a rather
smooth variation of line-of-sight and sky-projected velocities, which suggests
some connection of the environments and kinematics traced by both maser types.
The conical outflow model, previously proposed to account for the 12 GHz maser
kinematics in the northern clump, does not reproduce the new, accurate
measurements of 12 GHz maser proper motions and has to be rejected. We focus on
the subset of 12 GHz masers of the northern clump belonging to the "linear
structure at P.A. = 130-140 degree", whose regular variation of LSR velocities
with position presents evidence for some ordered motion. We show that the
3-dimensional velocities of this "linear distribution" of 12GHz masers can be
well fitted considering a flat, rotating disk, seen almost edge-on.
