Local magnitudes calculated at stations less than 10 km from earthquakes in the British Isles are up to one unit of magnitude higher than local magnitudes calculated at more distant stations. This causes a considerable overestimate of the event magnitude, particularly for small events, which are only recorded at short distances. Data from Central Italy and Norway show that the same problem also occurs in other regions, suggesting that this is a more general issue for local magnitude scales. We investigate the addition of a new exponential term to the general form of the local magnitude scale. This corrects for the higher-than-expected amplitudes at short hypocentral distances. We find that the addition of this new term improves magnitude estimates in the three studied regions and magnitudes at short distances are no longer overestimated. This allows the use of a single scale that can be used at all distances, with a smooth transition between short and long distances. For the UK, the amended scale is ML =log(amp) +1.11log(r)+0.00189r−1.16e−0.2r−2.09 and this is the scale now used by the British Geological Survey.