  We report a new scheme to create weakly bound Cs$_2$ molecules from an atomic
Bose-Einstein condensate. The method is based on switching the magnetic field
to a narrow Feshbach resonance and yields a high atom-molecule conversion
efficiency of more than 30%, a factor of three higher than obtained with
conventional magnetic-field ramps. The Cs$_2$ molecules are created in a single
$g$-wave rotational quantum state. The observed dependence of the conversion
efficiency on the magnetic field and atom density shows scattering processes
beyond two-body coupling to occur in the vicinity of the Feshbach resonance.
