Wavelet bases in rearrangement invariant function spaces

We point out that the well known characterization of $L^{p}$ spaces ($1<p<\infty$) in terms of orthogonal wavelet bases extends to any separable rearrangement invariant Banach function space $X$ on $R^{n}$ (equipped with Lebesgue measure) with nontrivial Boyd's indices. Moreover we show that such bases are unconditional bases of $X$.