A network of gravitational wave detectors is called redundant if, given thedirection to a source, the strain induced by a gravitational wave in one or moreof the detectors can be fully expressed in terms of the strain induced in othersin the network. Because gravitational waves have only two polarizations,any network of three or more differently oriented interferometers with similarobserving bands is redundant. The three-armed LISA space interferometerhas three outputs that are redundant at low frequencies. The two alignedLIGO interferometers at Hanford WA are redundant, and the LIGO detectorat Livingston LA is nearly redundant with either of the Hanford detectors.Redundant networks have a powerful veto against spurious noise, a linearcombination of the detector outputs that contains no gravitational wave signal.For LISA, this ‘null’ output is known as the Sagnac mode, and its use indiscriminating between detector noise and a cosmological gravitational wavebackground is well understood. But the usefulness of the null veto for groundbaseddetector networks has been ignored until now. We show that it shouldmake it possible to discriminate in a model-independent way between realgravitational waves and accidentally coincident non-Gaussian noise ‘events’ inredundant networks of two or more broadband detectors. It has been shownthat with three detectors, the null output can even be used to locate the directionto the source, and then two other linear combinations of detector outputs givethe optimal ‘coherent’ reconstruction of the two polarization components of thesignal. We discuss briefly the implementation of such a detection strategy inrealistic networks, where signals are weak, detector calibration is a significantuncertainty, and the various detectors may have different (but overlapping)observing bands.