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In this paper, the author defines the function B¯i,jδ,k(n), the number of singular overpartition pairs of n without multiples of k in which no part is divisible by δ and only parts congruent to ± i, ± j modulo δ may be overlined.

Andrews introduced to combinatorial objects, which he called singular overpartitions and proved that these singular overpartitions depend on two parameters δ and i can be enumerated by the function C¯δ,i(n), which gives the number of overpartitions of n in which no part divisible by δ and parts ≡ ± i(Mod δ) may be overlined.

Using classical spirit of q-series techniques, the author obtains congruences modulo 4 for B¯2,48,3(n), B¯2,48,5 and B¯2,412,3.

The results established in this work are extension to those proved in Andrews’ singular overpatition pairs of n.