  Pairing of composite fermions in half-filled Landau level state is reexamined
by solving the BCS gap equation with full frequency dependent current-current
interactions. Our results show that there can be a \emph{continuous} transition
from the Halperin-Lee-Read state to a chiral odd angular momentum Cooper pair
state for short-range contact interaction. This is at odds with the previously
established conclusion of first order pairing transition, in which the low
frequency effective interaction was assumed for the entire frequency range. We
find that even if the low frequency effective interaction is repulsive, it is
compensated by the high frequency regime, which is attractive. We construct the
phase diagrams and show that $\ell=1$ angular momentum channel is quite
different from higher angular momenta $\ell\ge 3$. Remarkably, the full
frequency dependent analysis applied to the bilayer Hall system with a total
filling fraction $\nu=\frac{1}{2}+\frac{1}{2}$ is quantitatively changed from
the previously established results but not qualitatively.
