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We call indexed-biharmonic maps, the solutions of a particular non linearelliptic PDE of order 4. This is a generalization of harmonic maps whichverifies that biharmonic maps are biharmonic of index 0. The goal of thisarticle is to study submanifolds of $\mathbb{S}^n$ whose inclusion is nonharmonic and indexed-biharmonic (i.e. proper indexed-biharmonic). We give somepseudo-umbilical and non pseudo-umbilical examples and we study the linkbetween the proper indexed-biharmonic submanifolds of $\mathbb{S}^n$ and theproper conformal-harmonic submanifolds of $\mathbb{S}^n$.

Exemples de sous vari\'et\'es de $\mathbb{S}^n$; les vari\'et\'es proprement biharmoniques avec indice et les vari\'et\'es proprement C--harmoniques