We　present　a　new　test　for　uniform　distribution　on　the　surface　of　a　unit　sphere　based　on　the　Moore-Penrose　inverse　of　the　covariance　matrix　of　the　uniform　distribution.　The　new　test　possesses　symmetry　which　improves　on　the　combination　tests　based　on　the　center　of　mass　and　the　moment　of　inertia.　The　asymptotic　chi-squared　distribution　of　the　test　statistic　is　obtained,　the　test　has　the　nice　properties　as　the　combination　tests　and　it　is　quite　easy　to　implement.