Complex-valued Hopfield associative memory (CHAM) is one of the most promising neural network models to deal with multilevel information. CHAM has an inherent property of rotational invariance. Rotational invariance is a factor that reduces a network's robustness to noise, which is a critical problem. Here, we proposed complex-valued bipartite auto-associative memory (CBAAM) to solve this reduction in noise robustness. CBAAM consists of two layers, a visible complex-valued layer and an invisible real-valued layer. The invisible real-valued layer prevents rotational invariance and the resulting reduction in noise robustness. In addition, CBAAM has high parallelism, unlike CHAM. By computer simulations, we show that CBAAM is superior to CHAM in noise robustness. The noise robustness of CHAM decreased as the resolution factor increased. On the other hand, CBAAM provided high noise robustness independent of the resolution factor.