The (5, 5)-point scheme of Kimble and White (1990) for discretising a parabolic partial differential equation is shown to be inherently (locally) unconditionally unstable, as is the corresponding five-point scheme for solving an ordinary differential equation. However, by casting the time-marching problem into a large matrix equation and terminating the system with some asymmetric backward differentiation (5, 5)-point discretisations, Kimble and White stabilised the system and achieved high-order accuracy using it. By reducing the number of points in time, the scheme could, in principle, be used to start a multi-level scheme such as BDF.