  We study the spin dynamics in a p-wave superconductor at the nesting vector
associated with $\alpha$ and $\beta$ bands in Sr$_2$RuO$_4$. We find a
collective mode at the nesting vector in the superconducting phase identified
as the odd-parity pairing state which breaks time reversal symmetry. This mode
in the spin channel only exists in the p-wave superconductor, not in s- or
d-wave superconductors. We propose that probing this mode would clarify the
pairing symmetry in Sr$_2$RuO$_4$. The possibility of second superconducting
phase transition is also discussed.
