In this paper a new fundamental solution for unsteady incompressible fluid problems is derived. The time dependent term is decomposed using suitable finite difference scheme. Hence, the unknown fluid velocity is directly incorporated into the problem differential operator converting the transient equations into steady state equations with new differential operator, to which the developed fundamental solution is derived. This is carried out within the context of penalty formulation of Navier-Stokes equations. The direct boundary integral equation is derived for the proposed method and used in the solution of the well-known Lid driven cavity problem with 2 different aspect ratios. The results demonstrate excellent agreement with previously published results.