An approach in the search for high temperature superconductors with a T c above 120 K without volatile toxic elements is proposed and its rationale is given. The compound system Ba 2 Ca n - 1 + x Cu n + y O z = (Ca x ,Cu y )Ba 2 Ca n - 1 Cu n O z with a T c up to 126 K has thus been successfully synthesized under high pressure and characterized. Another three superconducting phases at 90, 105, and 116 K, respectively, were also detected. The compound system offers a possibility for high temperature superconducting (HTSg) thin-film devices operable above 120 K, reachable in space by a passive cooler, when its stability is improved; and an opportunity to investigate the dimensionality effect on high temperature superconductivity.