We describe a search for the decay of the Z boson into pairs of doubly charged Higgs bosons with the Mark II detector operating at the SLAC Linear Collider. Each Higgs boson is assumed to decay into a same-sign leptonic pair. No event candidates are found in a sample of 528 Z decays. At the 95% confidence level, this result excludes the region of leptonic coupling gll3×10-7 and Higgs-boson mass 6.5MH 36.5 GeV/c2 for isotriplet (left-handed) Higgs bosons. Isosinglet (right-handed) Higgs bosons are excluded in the same gll interval and in the mass interval 7.3 MH 34.3 GeV/c2. © 1990 The American Physical Society.