Subjects have acute promyelocytic leukemia (APL) that has come back (relapsed) after initial treatment or has not gone away with initial therapy. This research study involves testing an investigational drug called Tamibarotene in combination with standard treatment for relapsed APL called arsenic trioxide. Tamibarotene has been approved in Japan to treat patients with relapsed APL since April 2005. Tamibarotene is in the same family of drugs as all-trans retinoic acid (ATRA), a medication that subjects received previously in their treatment. ATRA and tamibarotene both cause the APL cells to differentiate (or become) normal non-leukemia cells. Laboratory studies of tamibarotene have shown to be effective in APL. The purpose of this study is to determine if tamibarotene in combination with arsenic trioxide is safe and effective.