  We show analytically that particle trapping appears in a quantum process
called "quantum walk", in which the particle moves macroscopically correlating
to the inner states. It has been well known that a particle in the ``Hadamard
walk" with two inner states spreads away quickly on a line. In contrast, we
find one-dimensional quantum walk with multi-state in which a particle stays at
the starting point entirely with high positive probability. This striking
difference is explained from difference between degeneration of eigenvalues of
the time-evolution matrices.
