  We compute the decay rates for the exclusive decays $B^{\pm} \to
(\eta^{\prime},\eta) (K^{\pm}, K^{*\pm})$ and $B^{0}\to (\eta^{\prime},\eta)
(K^{0}, K^{*0})$ in a QCD-improved factorization framework by including the
contribution from the process $b\to sgg \to s (\eta^{\prime}, \eta)$ through
the QCD anomaly. This method provides an alternative estimate of the
contribution $b \to s c\bar{c} \to s(\eta,\eta^\prime)$ to these decays as
compared to the one using the intrinsic charm content of the $\eta^{\prime}$
and $\eta$ mesons determined through the decays $J/\psi \to (\eta,\eta^\prime
,\eta_c) \gamma$. The resulting branching ratios are compared with the CLEO
data on $B^{\pm} \to \eta^{\prime} K^{\pm}$ and $B^{0} \to \eta^{\prime} K^{0}$
and predictions are made for the rest.
