Based　on　the　hidden　conformal　symmetry,　some　authors　have　proposed　a　Harrison　metric　for　the　Schwarzschild　black　hole.　We　give　a　procedure　which　can　generate　a　family　of　Harrison　metrics　starting　from　a　general　set　of　SL(2,　R)　vector　fields.　By　analogy　with　the　subtracted　geometry　of　the　Kerr　black　hole,　we　find　a　new　Harrison　metric　for　the　Schwarzschild　case.　Its　conformal　generators　are　also　investigated　using　the　Killing　equations　in　the　near-horizon　limit.