An \(n\)-dimensional hypersurface \(M\) in the \((n+1)\)-dimensional unit sphere \(S^{n+1}\) is called a Willmore hypersurface if it is an extremal hypersurface of the Willmore functional \[ \int_{M}(S-nH^{2})^{n/2} dv, \] where \(S\) is the square of the length of the second fundamental form and \(H\) is the mean curvature of \(M\). Common examples of Willmore hypersufaces are the tori \(W_{m,n-m}=S^{m}(\sqrt{1-r^{2}})\times S^{n-m}(r)\), \(r^{2}=m/n\), \(1\leq m\leq n-1\), called Willmore tori by the author. After some technical preparations (Lemmas 2.1 and 2.2) and by computing the Euler-Lagrange equation of the Willmore functional, the author gives – in Theorem 1 – a characterization of Willmore hypersurfaces in \(S^{n+1}\). Then, an integral inequality of Simons’ type is proved in Theorem 3. In the case when \(S-nH^{2}<n\), Theorem 3 assures that either \(M\) is totally umbilical or has constant mean curvature. In the last section, the author gives a classification of isoparametric Willmore hypersurfaces.