real analysis – Convergent function sequence by point with a uniformly convergent subsequence.

Let $ f_n colon [0,1] to mathbb {R} $ be a sequence of continuous functions that converge point to a continuous function $ f $. Yes $ {f_n } $ has a uniformly convergent subsequence $ {f_ {n_k} } $, does that imply that $ f_n $ converges uniformly towards $ f $. If the answer is "no", please give me an example. Thanking you in advance.