We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L = 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Tc = 3.6403(2). A convincing finite-size scaling analysis of the model yields v = 0.9995(21), β/v =0.12400(17), γ/v = 1.75223(22),γ’/v = 1.7555(22), α/v = 0.00077(420) (scaling) and a/v = 0.0010(42) (hyperscaling).The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.