In　this　note,　we　revisit　the　single-index　model　with　heteroscedastic　error,　and　recommend　an　estimating　equation　method　in　terms　of　transferring　restricted　least　squares　to　unrestricted　least　squares:　the　estimator　of　the　index　parameter　is　asymptotically　more　efficient　than　existing　estimators　in　the　literature　in　the　sense　that　it　is　of　a　smaller　limiting　variance.　(C)　2010　Elsevier　Inc.　All　rights　reserved.