  We discuss multicritical behavior of $c=1$ matrix model, extending the recent
work of ref. \cite{CIO} on a nonperturbative completion of the density of
states function. For the odd orders of multicriticality, we are able to
determine the higher genus contributions and a nonperturbative completion from
the WKB wave function of the multicritical periodic potential. The expression
for the contributions as a function of the scaled chemical potential is found
to be the same as the one at the lowest critical point. We point out a strange
scaling behavior.
