  The beta-neutrino correlation coefficient, $a_{\beta\nu}$, is measured in
sodium-21 by detecting the time-of-flight of the recoil nucleus detected in
coincidence with the atomic electrons shaken off in beta decay. The sample of
sodium-21 is confined in a magneto-optic trap. High detection efficiency allows
low trap density, which suppresses the photoassociation of molecular sodium,
which can cause a large systematic error. Suppressing the fraction of trapped
atoms in the excited state using a dark trap also reduces the photoassociation
process, and data taken with this technique are consistent. The largest
remaining systematic uncertainties come from the measurement of the position
and size of the atom trap, and the subtraction of background. We find
$a_{\beta\nu}$ =0.5502(60), in agreement with the Standard Model prediction of
$a_{\beta\nu}$ =0.553(2), and disagreeing with a previous measurement which was
susceptible to an error introduced by the presence of molecular sodium.
