A subcouple \((F_0, F_1)\) of a couple \((E_0, E_1)\) of quasi-Banach spaces is said to be \(K\)-closed if any decomposition \(f=e_0 + e_1, e_i \in E_i\) of a vector \(f \in F_0 + F_1\) gives rise to a decomposition \(f= f_0 +f_1\) with \(f_i \in F_i\) and \( \| f_i \|_{F_i} \leq C \| e_i \|_{E_i}, i=1,2\). Let \({ \mathbb H}^p( {\mathbb R}^n)\) be the real variable Hardy space in the sense of Stein-Weiss. The author proves the following: the couple of Hardy spaces \(( {\mathbb H}^{p_1}( {\mathbb R}^n), {\mathbb H}^{p_2}( {\mathbb R}^n))\) is \(K\)-closed in the couple of corresponding Lebesgue spaces \(( {\mathbb L}^{p_1}( {\mathbb R}^n), {\mathbb L}^{p_2}( {\mathbb R}^n))\) for \(\frac{n-1}{n} < p_1 < p_2 \leq \infty.\) This result was proved by S. V. Kisliakov [in: Function spaces, interpolation spaces, and related topics. Proceedings of the workshop, Haifa, Israel, 1995. Ramat Gan: Bar-Ilan University/distr. by the American Mathematical Society, Isr. Math. Conf. Proc. 13, 102–140 (1999; Zbl 0956.46018)] for \(1 \leq p_1\).