In　this　paper,　a　fourth-moment　transformation　technique　is　proposed　to　transform　correlated　nonnormal　random　variables　into　independent　standard　normal　ones.　The　procedure　mainly　includes　two　steps:　First,　the　correlated　nonnormal　random　variables　are　transformed　into　correlated　standard　normal　ones　using　the　fourth-moment　transformation,　where　the　complete　mathematical　formula　of　the　correlation　coefficient　in　standard　normal　space,　i.e.,　equivalent　correlation　coefficient,　is　proposed　and　the　upper　and　lower　bounds　of　original　correlation　coefficient　are　identified　to　ensure　the　transformation　executable;　Second,　the　correlated　standard　normal　random　variables　are　transformed　into　independent　standard　normal　ones　using　Cholesky　decomposition.　For　the　cases　of　original　correlation　matrix　with　very　small　eigenvalues,　the　equivalent　correlation　matrix　might　become　a　nonpositive　semidefinite　matrix.　A　recently　developed　method　for　solving　the　problem　is　adopted　to　make　Cholesky　decomposition　ready.　A　first-order　reliability　method　(FORM)　for　structural　reliability　analysis　involving　correlated　random　variables　is　developed　using　the　proposed　transformation　technique.　Several　numerical　examples　are　presented　to　demonstrate　the　efficiency　and　accuracy　of　the　proposed　method　for　structural　reliability　assessment　considering　correlated　random　variables.