  Let $E$ be a real Banach space. For $x,y \in E,$ we follow R.James in saying
that $x$ is orthogonal to $y$ if $\|x+\alpha y\|\geq \|x\|$ for every $\alpha
\in R$. We prove that every operator from $E$ into itself preserving
orthogonality is an isometry multiplied by a constant.
