The Unconstrained Binary Quadratic Programming (UBQP) is a NP-hard problem able to represent a wide range of combinatorial optimization problems. The problem has grown in importance due to its potential application and its computational challenge. Recently, the problem was extended to multiobjective case (mUBQP). On the other hand, Ant Colony Optimization Algorithms (ACO) have been widely used to solve several combinatorial single and multiobjective problems. Moreover, some works have been proposed to use an ACO variation called Binary Ant Colony Optimization (BACO) due to its simple structure and achieving good results. Therefore, in this study, a Multiobjective Binary ACO based on decomposition algorithm is proposed. This algorithm, named MOEA/D-BACO, was designed using concepts of MOEA/D (Multiobjective Evolutionary Algorithm based on Decomposition) and ACO that decomposes a problem into a set of scalar optimization sub problems. Experiments have been conducted to compare MOEA/D-BACO to NSGAII and MOEA/D on a set of instances of mUBQP. The results show that the proposed algorithm outperforms NSGAII and is competitive with MOEA/D finding a good approximation to the entire Pareto front.