The congruence of certain restricted partition functions known as regular bipartition is discussed in this paper. We particularly investigate the (2,β)-regular bipartitions of n, denoted by B2,β(n), and establish certain congruences for B2,β(n) when β ≥ 3. We derive infinite families of congruences modulo 4 for the (2; 3)-regular bipartition. We also obtain a generalisation of the regular bipartition for modulo p and p².