Laguerre-FDTD is an unconditionally stable finite-difference time-domain (FDTD) scheme that uses La guerre polynomials for transient simulation. Laguerre-FDTD has been shown to be significantly faster than conventional FDTD scheme. However, prior work on Laguerre-FDTD for EM simulation has the limitation of being able to simulate only for a certain timeduration and can only be applied to structures where fields decay to zero within a certain time-duration. In this paper, a solution has been proposed to overcome these limitations, so that transient EM simulation can be done accurately for all time and for all types of structures. An EM test-case in 2D has been presented to illustrate the extended Laguerre-FDTD method.