We present a search for a quasi-stable doubly-charged Higgs particle at CDF using the Fermilab Tevatron for (radical)s = 1.96 TeV. The data presented are from approximately 290 pb(sup -1) of integrated luminosity collected using the upgraded Run 2 Collider Detector at Fermilab. These data were taken between February, 2002 and February, 2004. The long-lived decay products of Z's are selected in the central detector region ('(eta)' < 1.0). They select events triggered on a muon candidate having p(sub T) > 18 GeV in the event. After offline reconstruction, they require two isolated tracks (p(sub T) > 20 GeV) in the event, one of which points to a stub in a muon detector. Since the search is based on the increased ionization a doubly-charged particle would produce as it passes through the detector, they require that both tracks be highly ionizing for an event to be selected as a H(sup (+-)(+-)) candidate. No such candidates are observed in the data. They set a lower mass limit of 146 GeV on a quasi-stable H(sup (+-)(+-)) boson.