A method of calculating the velocity autocorrelation function psi (t) in a monatomic classical liquid is developed, using directly the equation of motion of an atom in a liquid and a procedure which involves decoupling a statistical average. This leads to an equation of the form (d/dt) psi (t)+ integral 0td tau K(t- tau ) psi ( tau )=0 and gives a prescription for calculating the 'memory' function K(t) in terms of the interatomic potential, the static pair correlation function and the selfcorrelation function Gs. Within the Gaussian approximation, Gs depends on psi (t) and the calculation therefore gives an approximately selfconsistent means of determining the latter. The first approximation to the solution, which involves replacing Gs by its ideal gas value, leads to the well known linear trajectory approximation for the diffusion coefficient and indicates that the method will give results which supersede this approximation.