The orientation of an embedded submanifold of $\mathbb R^n$

Question

Assume $M$ is an embedded submanifold of $\mathbb R^n$ with codimension 1, by a specific coordinate of $\mathbb R^n$ $\{x_1,\dots,x_n\}$ in an area $U$, the $M\cap U$ has coordinate $\{x_1,\dots,x_{n-1}\}$. Under this coordinate,the orientation of $\mathbb R^n$ can be determined by the standard volume form $dx_1\wedge dx_2\wedge\dots\wedge dx_n$, so the standard volume form of $dx_1\wedge dx_2\wedge\dots\wedge dx_{n-1}$, thus the submanifold of $\mathbb R^n$ is orientable? Am I right?