  The determination of the critical exponents by means of the Exact
Renormalizion Group approach is still a topic of debate. The general flow
equation is by construction scheme independent, but the use of the truncated
derivative expansion generates a model dependence in the determination of the
universal quantities. We derive new nonperturbative flow equations for the
one-component, $Z_2$ symmetric scalar field to the next-to-leading order of the
derivative expansion by means of a class of proper time regulators. The
critical exponents $\eta$, $\nu$ and $\omega$ for the Wilson-Fisher fixed point
are computed by numerical integration of the flow equations, without resorting
to polynomial truncations. We show that by reducing the width of the cut-off
employed, the critical exponents become rapidly insensitive to the cut-off
width and their values are in good agreement with the results of entirely
different approaches.
