We present alignment refinement by mining coupled residues (ARMiCoRe), a novel approach to a classical bioinformatics problem, viz., multiple sequence alignment (MSA) of gene and protein sequences. Aligning multiple biological sequences is a key step in elucidating evolutionary relationships, annotating newly sequenced segments, and understanding the relationship between biological sequences and functions. Classical MSA algorithms are designed to primarily capture conservations in sequences whereas couplings, or correlated mutations, are well known as an additional important aspect of sequence evolution. (Two sequence positions are coupled when mutations in one are accompanied by compensatory mutations in another). As a result, better exposition of couplings is sometimes one of the reasons for hand-tweaking of MSAs by practitioners. ARMiCoRe introduces a distinctly pattern mining approach to improving MSAs: using frequent episode mining as a foundational basis, we define the notion of a coupled pattern and demonstrate how the discovery and tiling of coupled patterns using a max-flow approach can yield MSAs that are better than conservation-based alignments. Although we were motivated to improve MSAs for the sake of better exposing couplings, we demonstrate that our MSAs are also improvements in terms of traditional metrics of assessment. We demonstrate the effectiveness of ARMiCoRe on a large collection of data sets.