  We apply a new updating algorithm scheme to investigate the critical behavior
of the two-dimensional ferromagnetic Ising model on a triangular lattice with
nearest neighbour interactions. The transition is examined by generating
accurate data for large lattices with $L=8,10,12,15,20,25,30,40,50$. The spin
updating algorithm we employ has the advantages of both metropolis and
single-update methods. Our study indicates that the transition to be continuous
at $T_c=3.6403(2)$. A convincing finite-size scaling analysis of the model
yield $\nu=0.9995(21)$, $\beta/\nu=0.12400(18)$, $\gamma/\nu=1.75223(22)$,
$\gamma'/\nu=1.7555(22)$, $\alpha/\nu=0.00077(420)$ (scaling) and
$\alpha/\nu=0.0010(42)$(hyperscaling) respectively. Estimates of present scheme
yield accurate estimates for all critical exponents than those obtained with
Monte Carlo methods and show an excellent agreement with their well-established
predicted values.
