In this paper we prove the following result. Let $s$ be an infinite word on a finite alphabet, and $N\geq 0$ be an integer. Suppose that all left special factors of $s$ longer than $N$ are prefixes of $s$, and that $s$ has at most one right special factor of each length greater than $N$. Then $s$ is a morphic image, under an injective morphism, of a suitable standard Arnoux-Rauzy word.