  We report unexpected fluctuations in the positions of Coulomb blockade peaks
at high magnetic fields in a small Si quantum dot. The fluctuations have a
distinctive saw-tooth pattern: as a function of magnetic field, linear shifts
of peak positions are compensated by abrupt jumps in the opposite direction.
The linear shifts have large slopes, suggesting formation of the ground state
with a non-zero angular momentum. The value of the momentum is found to be well
defined, despite the absence of the rotational symmetry in the dot.
