We investigate the linear stability of a shocked accretion flow onto a black
hole in the adiabatic limit. Our linear analyses and numerical calculations
show that, despite the post-shock deceleration, the shock is generally unstable
to non-axisymmetric perturbations. The simulation results of Molteni, T\'oth &
Kuznetsov can be well explained by our linear eigenmodes. The mechanism of this
instability is confirmed to be based on the cycle of acoustic waves between the
corotation radius and the shock. We obtain an analytical formula to calculate
the oscillation period from the physical parameters of the flow. We argue that
the quasi-periodic oscillation should be a common phenomenon in accretion flows
with angular momentum.Comment: 14 pages, 7 figures, accepted for publication in MNRA