We demonstrate that optical fibre tapers can be utilised as a new means for achieving self-aligned beam expansion in single-mode fibres. These devices, which have a standard single-mode geometry at one end and gradually increase to a core size in the order of 100 μm at the other end, have greatly reduced sensitivities to lateral and axial displacements and an excess coupling loss between two tapers of less than 0.1 dB.