  The renormalization group flow equation obtained by means of a proper time
regulator is used to calculate the two loop beta function and anomalous
dimension eta of the field for the O(N) symmetric scalar theory. The standard
perturbative analysis of the flow equation does not yield the correct results
for both beta and eta. We also show that it is still possible to extract the
correct beta and eta from the flow equation in a particular limit of the
infrared scale. A modification of the derivation of the Exact Renormalization
Group flow, which involves a more general class of regulators, to recover the
proper time renormalization group flow is analyzed.
