One of the main techniques for the Finite-Difference Time-Domain (FDTD) analysis of dispersive media is the Recursive Convolution (RC) method. The idea here proposed for calculating the updating FDTD equation is based on the Laplace transform and is applied to the Drude dispersion case. A modified RC-FDTD algorithm is then deduced. We test our algorithm by simulating gold and silver nanospheres exposed to an optical plane wave and comparing the results with the analytical solution. The modified algorithm guarantees a better overall accuracy of the solution, in particular at the plasmonic resonance frequencies.