  The effect of nuclear superfluidity on antimagnetic rotation bands in
$^{105}$Cd and $^{106}$Cd are investigated by the cranked shell model with the
pairing correlations and the blocking effects treated by a particle-number
conserving method. The experimental moments of inertia and the reduced $B(E2)$
transition values are excellently reproduced. The nuclear superfluidity is
essential to reproduce the experimental moments of inertia. The two-shears-like
mechanism for the antimagnetic rotation is investigated by examining the shears
angle, i.e., the closing of the two proton hole angular momenta, and its
sensitive dependence on the nuclear superfluidity is revealed.
