Summary: The paper generalizes \(\rho\) order of algebroid functions to \( (m,n,\rho)\) order of algebroid functions and it constructs some examples of algebroid functions without singular direction, and proves that every \(v\)-value algebroid function with finite positive order of growth must posses the maximality Borel directions outside \(2v\) exceptional values at most. If \(\varlimsup\limits_{r\rightarrow \infty}\dfrac{T (r,w)}{\ln^2 r}=\infty, w (z)\) exits a weak Borel direction at least.