In　this　paper,　an　efficient　and　explicit　technique　is　proposed　for　transforming　correlated　non-normal　random　variables　into　independent　standard　normal　variables　based　on　the　three-parameter　(3P)　lognormal　distribution.　In　contrast　with　the　classic　Nataf　transformation,　the　derived　equivalent　correlation　coefficient　in　non　orthogonal　standard　normal　space　of　the　proposed　transformation　is　expressed　as　an　explicit　formula,　thereby　avoiding　tedious　iteration　algorithm　or　multifarious　empirical　formulas.　Meanwhile,　the　applicable　range　of　the　original　correlation　coefficient　is　determined　based　on　fundamental　properties　of　the　proposed　expression　of　correlation　distortion　and　the　definition　of　correlation　coefficient.　The　proposed　transformation　requires　only　the　first　three　moments　(i.e.,　mean,　standard　deviation,　and　skewness)　of　basic　random　variables,　as　well　as　their　correlation　matrix.　Therefore,　the　proposed　transformation　can　also　be　applied　even　when　the　joint　distribution　or　marginal　distributions　of　the　basic　random　variables　are　unknown.　Several　numerical　examples　are　presented　to　demonstrate　the　user-friendliness,　efficiency,　and　accuracy　of　the　proposed　transformation　applied　in　structural　reliability　analysis　involving　correlated　non-normal　random　variables.