In this note, we shall give a description of ($\alpha ,\beta $)-derivations $\delta ,g$ and $h$ of a prime ring $R$ satisfying $\delta (x) = ag(x) + h(x)b$ for all $x\in U$, where $a$ and $b$ are some fixed noncentral elements of $R$ and $U$ a nonzero ideal of $R$. This result generalizes some known results.