A readout method based on fast waveform digitalization is proposed which improves the performance of large multiwire proportional chambers (MWPCs) with delay-line readout. Atmospheric muon detection data are presented, obtained with a 1 mtimes1 m, 200 wire, MWPC and two plastic scintillators, having the same sensitive area, used for muon identification purposes. The performance of two alternative data acquisition configurations is compared: the standard one, based on analog constant fraction discriminators (CFDs), and one using 5 GS/s waveform digitizers in which a CFD-like analysis is performed offline. The latter is shown to provide better, and more uniform, space resolution, allowing to correct position-dependent rise-time variations across the detector. The new technique is applicable to low count-rate applications, such as muon attenuation measurements in large matter volumes