  In this article, by comparing the characteristic functions, we prove that for
any $\nu$-valued algebroid function $w(z)$ defined in the unit disk with
$\limsup_{r\to1-}T(r,w)/\log\frac{1}{1-r}=\infty$ and the hyper order
$\rho_2(w)=0$, the distribution of the Borel radius of $w(z)$ and $w'(z)$ is
the same. This is the extension of G. Valiron's conjecture for the meromorphic
functions defined in $\widehat{\mathbb{C}}$.
