Suppose $(E,⟨.,.⟩)$ is an inner product space and $u\in \mathrm{H}\mathrm{o}\mathrm{m}(E)$, such that $\mathrm{i}\mathrm{m}u$ is non-degenerated. Then there is an orthogonal decomposition: $E=\mathrm{i}\mathrm{m}u\oplus \ker u^{\ast }$. Moreover $\mathrm{i}\mathrm{m}u$ is non-degenerated iff $\ker u^{\ast }$ is non-degenerated.