Tight junctions consist of a network of sealing strands that create selective ion permeability barriers between adjoining epithelial or endothelial cells. The current model for tight junction strands consists of paired rows of claudins (Cldn) coupled by a cis interface (X-1) derived from crystalline Cldn15. Here we show that tight junction strands exhibit a broad range of lateral bending, indicating diversity in cis interactions. By combining protein–protein docking, coevolutionary analysis, molecular dynamics, and a mutagenesis screen, we identify a new Cldn–Cldn cis interface (Cis-1) that shares interacting residues with X-1 but has an ~ 17° lateral rotation between monomers. In addition, we found that a missense mutation in a Cldn14 that causes deafness and contributes stronger to Cis-1 than to X-1 prevents strand formation in cultured cells. Our results suggest that Cis-1 contributes to the inherent structural flexibility of tight junction strands and is required for maintaining permeability barrier function and hearing.