In this work, we propose an improved methodology to compute the intrinsic friction coefficient at the liquid-solid (L-S) interface based on the theoretical model developed by Hansen et al. [Phys. Rev. E 84, 016313 (2011)]. Using equilibrium molecular dynamics, we apply our method to estimate the interfacial friction for a simple Lennard-Jones system of argon confined between graphene sheets and a system of water confined between graphene sheets. Our new method shows smaller statistical errors for the friction coefficient than the previous procedure suggested by Hansen et al. Since we only use the interfacial particles, the interfacial friction calculated using our method is solely due to the wall-fluid interactions and is devoid of bulk fluid contributions. The intrinsic nature of the friction coefficient has been validated by measuring the friction coefficient at different interfaces and channel sizes and against direct non-equilibrium molecular dynamics measurements. Our improved methodology is found to be more reliable than the existing equilibrium and non-equilibrium methods and does not suffer from the well-known convergence and correlation-time ambiguities in the methods formulated along Green-Kubo-like ideas.