The paper deals with Whitney convergence of sequences in \(C(X,Y),\) where \(X\) is a normal topological space and \((Y,d)\) is a metric space. By definition a sequence \((f_{n})_n\) is said to be Whitney convergent to \(f\) if for any positive real valued continuous function \(\varphi\) there exists \(n_0 \in \mathbb{N}\) such that \(d(f_n(x),f(x)) < \varphi(x)\) for each \(x \in X\) and \(n \geq n_0\). The main theorem of the paper states the following equivalent description. \((f_{n})_n\) is said to be Whitney convergent to \(f\) if and only if it is uniformly convergent to \(f\) and there exists a countably compact subset \(K\) in \(X\) such that if \(U\) is any neighborhood of \(K\) then there exists \(n_0 \in \mathbb{N}\) for which \(f_{n} |_{(X \setminus U)} = f |_{ (X \setminus U)}\) whenever \(n \geq n_0.\)