  In this work the two-dimensional Ising model with nearest- and
next-nearest-neighbor interactions is revisited. We obtain the dynamic critical
exponents $z$ and $\theta$ from short-time Monte Carlo simulations. The dynamic
critical exponent $z$ was obtained from the time behavior of the ratio $F_2=<
M^2>_{m_0=0}/< M>^2_{m_0=1}\sim t^{d/z}$, whereas the non-universal exponent
$\theta$ was estimated from the time correlation of the order parameter
$<M(0)M(t)>\sim t^{\theta}$, where $M(t)$ is the order parameter at instant
$t$, $d$ is the dimension of the system and $<(...)>$ is the average of the
quantity $(...)$ over different samples. We have also obtained the static
critical exponents $\beta$ and $\nu$ by investigating the time behavior of the
magnetization.
