  The mass-correction function is evaluated for selected excited states of the
hydrogen molecule within a single-state non-adiabatic treatment. Its
qualitative features are studied under the avoided crossing of the $EF$ with
the $GK$ state and also for the outer well of the $H\bar{H}$ state. For the
$H\bar{H}$ state, a negative mass correction is obtained for the vibrational
motion near the outer minimum, which accounts for most of the deviation between
experiment and earlier theoretical work.
