Let Hn denote the Heisenberg group. It is shown that under certain conditions the wavelet system {ψ j;k;l;m: k; ε Zn; j;m ε Z} on Hn arising from integer translations and nonisotropic dilations forms a Schauder basis for its closed linear span in L2(Hn) if and only if the function satisfies the Muckenhoupt A2 condition, where B2 denotes the class of Hilbert-Schmidt operators on L2(Rn). © Instytut Matematyczny PAN, 2019.