# Is Frenet-Serret frame valid for non-natural parametrized curves when one normalizes the tangent vector?

When one have a curve $\beta(s)$ which is parametrized by arc length (has natural parametrization) one is able to obtain the tangent, normal and binormal vectors by using Frenet-Serret frame equations:

$T = \beta'(s)$, $N=\frac{T'(s)}{|T'(s)|}$, $B = T \times N$

But are those formulas valid for non-regular parametrizations when one normalizes the tangent vector?

$T=\frac{\beta'(s)}{|\beta'(s)|}$, $N$ and $B$ are calculated as above.