If $\{h_m\}_{m \in \mathbb{N}}$ is a basis of an Hilbert space, is it possible $\inf_{m \in \mathbb{N}} \|h_m\| = 0$

Question

Let $H$ be an Hilbert space over $\mathbb{C}$ and let $\{h_m\}_{m \in \mathbb{N}}$ be an its basis.

Is it possible that $\inf_{m \in \mathbb{N}} \|h_m\| = 0$

Thanks.