Summary: Necessary and sufficient conditions are stated and proved for a system of functions \(\psi_{j,k}(s)= 2^{j/2} \psi(2^j s- k)\), \(j,k\in {\mathbf Z}\), to form a frame of wavelets in the Hardy space \({\mathbf H}^{2+}\). These conditions are expressed in terms of the Fourier transform \(\widehat\psi\) of \(\psi\). Special attention is paid to functions \(\widehat\psi\) whose support is contained in the intervals \([0,2]\), \([1,4]\) or that are step functions.