This paper proposes a new explanation of the job quality issue in search and matching models, which is not based on market externalities but on strategic interactions within firms through the intrafirm bargaining process. We develop a matching and intrafirm bargaining model in which large firms hire workers on a frictional labour market and decide to destroy low productivity job-worker matches. The coexistence of entry and exit flows of workers in a large firm gives rise to a specific interaction between the firing decision and the intrafirm bargaining process on wages, which causes inefficient decisions to be made on hiring and firing. The sources of inefficiency in this economy are (i) the well-known quantitative effect of intrafirm bargaining, namely the excessive size of the firms concerned, and (ii) a new quality effect, namely the poor quality of the job-worker matches selected by firms.