Wiping compositions are disclosed well suited for destroying various different microorganism very quickly. The wiping composition contains a tertiary alkyl amine biocide in combination with one or more other components. The wiping composition, for instance, may contain a pH adjustor, chelating agent, one or more surfactants, and water as a liquid carrier. In one embodiment, the composition can be formulated to contain various organic solvents that increase efficacy against mycobacteria. The wiping composition is particularly well suited to being impregnated into a disposable wipe.