existence of a 1-form

Question

Suppose $L$ is a fibered link in $S^3$ and consider the fibration $f:S^3-L\to S^1$. Is it possible to write down the 1-form $df$ in the form $df=md\mu+ld\lambda$ near each component of $L$, for which $\mu$ and $\lambda$ are standard meridian and longitude induced by the fibration and $m,l$ are constants?