This paper presents a new finite-volume discretization of a generalised Lattice Boltzmann equation (LBE) on unstructured grids. This equation is the continuum LBE, with the addition of a second order time derivative term (memory), and is derived from a second-order differential form of the semi-discrete Boltzmann equation in its implicit form. The new scheme, named unstructured lattice Boltzmann equation with memory (ULBEM), can be advanced in time with a larger time-step than the previous unstructured LB formulations, and a theoretical demonstration of the improved stability is provided. Taylor vortex simulations show that the viscosity is the same as with standard ULBE and demonstrates that the new scheme improves both stability and accuracy. Model validation is also demonstrated by simulating backward-facing step flow at low and moderate Reynolds numbers, as well as by comparing the reattachment length of the recirculating eddy behind the step against experimental and numerical data available in literature.