Haar bases for L²(mathbb{Q}₂²) generated by one wavelet function

The concept of $p$-adic quincunx Haar MRA was introduced and studied in~\cite{KS10}. In contrast to the real setting, infinitely many different wavelet bases are generated by a $p$-adic MRA. We give an explicit description for all wavelet functions corresponding to the quincunx Haar MRA. Each one generates an orthogonal basis, one of them was presented in~\cite{KS10}. A connection between quincunx Haar bases and two-dimensional separable Haar MRA is also found.