  A decaying particle that dominates the energy density of the universe and
then decays with a lifetime $\sim 10^{-1}$ sec into
electromagnetically-interacting particles can heat the background electron
neutrinos more than the $\mu$ and $\tau$ neutrinos, resulting in a decrease in
the primordial $^4$He abundance. Previous calculations of this effect assumed
sudden decoupling of the neutrinos from the electromagnetic plasma. Here we
repeat this calculation using an improved (although still approximate)
treatment of the energy flow from the blackbody radiation into the various
neutrino components. We find that with our improved calculation, the reduction
in the primordial $^4$He is not as large as had been previously thought, but it
occurs over a larger range in decaying particle lifetime $\tau$. The reduction
in $^4$He can be as large as $\Delta Y = -0.01$ for $\tau = 0.1 - 0.7$ sec.
