We revise the process of muon pair production by high-energy muons in rock using the recently published cross-section. The three-dimensional Monte Carlo code MUSIC has been used to obtain the characteristics of the muon bundles initiated via this process. We have compared them with those of conventional muon bundles initiated in the atmosphere and shown that large underground detectors, capable of collecting hundreds of thousands of multiple muon events, can discriminate statistically muon induced bundles from conventional ones. However, we find that the enhancement of the measured muon decoherence function over that predicted at small distances, recently reported by the MACRO experiment, cannot be explained by the effect of muon pair production alone, unless its cross-section is underestimated by a factor of 3.