Summary: In this paper, we introduce generalized contraction condition for two pairs \((F, f)\) and \((G, g)\) of maps \(F, G : X \times X \rightarrow X\), \(f, g : X \rightarrow X\) where \(X\) is a \(b\)-metric space and prove the existence and uniqueness of common coupled fixed points of these two pairs under the assumptions that these pairs are \(w\)-compatible and satisfying generalized contraction condition by restricting the completeness of \(X\) to its subspace. We draw some corollaries from our main results and provide examples in support of our results.