  We calculate the complete ${\cal O}(\alpha_s)$ corrections to the quark decay
$b\to ccs$ taking full account of the quark masses, but neglecting penguin
contributions. For a c to the b quark mass ratio $m_c/m_b= 0.3$ and a strange
quark mass of $0.2\,$GeV, we find that the next-to-leading order (NLO)
corrections increase $\Gamma(b\to ccs)$ by $(32\pm 15)\%$ with respect to the
leading order expression, where the uncertainty is mostly due to scale- and
scheme-dependences. Combining this result with the known NLO and
non-perturbative corrections to other B meson decay channels we obtain an
updated value for the semileptonic branching ratio of B mesons, $B_{SL}$, of
$(12.0\pm 1.4)\% $ using pole quark masses and $(11.2\pm 1.7)\% $ using running
$\overline{\mbox{MS}}$ masses.
