The performance of the labor market depends not only on the quantity of jobs in the economy, but also on the quality of jobs. This paper proposes a new theoretical explanation of the job quality issue in search and matching models. We develop a matching and intra-firm bargaining model in which large firms hire workers and decide to destroy low-productivity job–worker matches. The sources of inefficiency include the well-known quantitative effect of intra-firm bargaining, namely, the excessive size of the firms concerned; and a new quality effect, namely, the poor quality of the job–worker matches selected by firms.