Two-agent combination trials have recently attracted enormous attention in oncology research. There are several strong motivations for combining different agents in a treatment: to induce the synergistic treatment effect, to increase the dose intensity with nonoverlapping toxicities, and to target different tumor cell susceptibilities. To accommodate this growing trend in clinical trials, we propose a Bayesian adaptive design for dose finding based on latent 2 x 2 tables. In the search for the maximum tolerated dose combination, we continuously update the posterior estimates for the unknown parameters associated with marginal probabilities and the correlation parameter based on the data from successive patients. By reordering the dose toxicity probabilities in the two-dimensional space, we assign each coming cohort of patients to the most appropriate dose combination. We conduct extensive simulation studies to examine the operating characteristics of the proposed method under various practical scenarios. Finally, we illustrate our dose-finding procedure with a clinical trial of agent combinations at M. D. Anderson Cancer Center.