A　conjugation　on　a　Hilbert　space　H　means　an　antilinear　bounded　operator　that　the　squares　to　the　identity,　which　generalizes　the　traditional　conjugation　on　complex　Euclidean　spaces.　In　this　paper,　with　the　help　of　normalized　conjugation　we　introduce　the　notion　of　conjugate　phase　retrieval　on　general　Hilbert　spaces.　We　characterize　frames　that　do　conjugate　phase　retrieval;　prove　that　every　conjugate　phase　retrieval　frame　for　H　consisting　of　all　real　vectors　has　the　complement　property　in　H,　and　the　converse　is　true　if　dim(H)　＜=　2;　and　also　prove　that　a　small　perturbation　of　conjugate　phase　retrieval　frame　still　gives　a　conjugate　phase　retrieval　frame　if　dim(H)　＜　infinity,　but　it　is　false　if　dim(H)　=　infinity.