  We study the pairing symmetry of the interlayer paired state of composite
fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory,
the effect of the long-range Coulomb interaction and the internal Chern-Simons
gauge fluctuation is analyzed with the random-phase approximation beyond the
leading order contribution in small momentum expansion, and we observe that the
interlayer paired states with a relative angular momentum $l=+1$ are
energetically favored for filling $\nu=\frac{1}{2}+\frac{1}{2}$ and
$\frac{1}{4}+\frac{1}{4}$. The degeneracy between states with $\pm l$ is lifted
by the interlayer density-current interaction arising from the interplay of the
long-range Coulomb interaction and the Chern-Simons term in the HLR theory.
