We have developed a new formalism where we have recast the plane-wave pseudopotential method in terms of non-orthogonal localised functions instead of Kohn-Sham bands. A key ingredient for computationally efficient calculations with our approach is the restriction of the local functions both in real and in reciprocal space. We have written a new code to implement and test this approach. Even though it is equivalent to plane-waves, our method performs calculations directly with localised functions without ever resorting to Kohn-Sham states. As a consequence it could be more suitable for application to fields such as the theory of electric polarisation of insulators. However we anticipate that the main use of this approach will be in density-functional calculations on insulators whose cost scales linearly with the size of the system. Its extension to linear-scaling calculations requires the reduction of the elements of the density kernel by truncation. Our test calculations on a variety of systems confirm that such a linear-scaling method should be directly comparable to traditional plane-waves. Advantages of our approach include high accuracy, applicability to any lattice symmetry and systematic basis set improvement controlled by the kinetic energy cutoff.