Context. We present a new event of quasi-periodic wave trains observed in EUV wavebands that rapidly propagate away from an active region after a flare. Aims. We measured the parameters of a wave train observed on 7 December 2013 after an M1.2 flare, such as the phase speeds, periods and wavelengths, in relationship to the local coronal environment and the energy sources. Methods. We compared our observations with a numerical simulation of fast magnetoacoustic waves that undergo dispersive evolution and leakage in a coronal loop embedded in a potential magnetic field. Results. The wave train is observed to propagate as several arc-shaped intensity disturbances for almost half an hour, with a speed greater than 1000 km s −1 and a period of about 1 min. The wave train followed two different patterns of propagation, in accordance with the magnetic structure of the active region. The oscillatory signal is found to be of high-quality, i.e. there is a large number (10 or more) of subsequent wave fronts observed. The observations are found to be consistent with the numerical simulation of a fast wave train generated by a localised impulsive energy release. Conclusions. Transverse structuring in the corona can efficiently create and guide high-quality quasi-periodic propagating fast wave trains.