It is well-known in the literature on Hardy spaces that the Hardy spaces H^p, 0<p<1, are not normable. However, none of the sources offer proofs of this fact. In 1953, Livingston published an article demonstrating this using a convexity argument based on a theorem by Kolmogorov. In this talk, we will present a direct proof based on a counterexample of the non-normability of the Hardy spaces H^p, 0<p<1. This is a joint work with my thesis advisor Dragan Vukotic.