  We consider the evolution of baryon number $B$ in the early universe under
the influence of rapid sphaleron interactions and show that $B$ will remain
nonzero at all times even in the case of $B-L = 0$. This result arises due to
thermal Yukawa interactions that cause nonidentical dispersion relations
(thermal masses) for different lepton families. We point out the relevance of
our result to the Affleck-Dine type baryogenesis.
