Bidirectional associative memory is a hetero-associative memory which has two layers. It cannot deal with one-to-many associations. Osana et al. proposed a chaotic bidirectional associative memory which can deal with one-to-many association due to the invisible part. Moreover, Yano and Osana proposed a chaotic complex-valued bidirectional associative memory whose all neurons are complex-valued. However, it associates not only training patterns but also patterns referred to as rotated patterns. Thus, the conventional chaotic complex-valued bidirectional associative memory model is insufficient for applications. In this paper, we propose a chaotic complex-valued bidirectional associative memory with a real-valued invisible part. It can prevent the rotated patterns from appearing. Our proposed model almost associates only training patterns and is promising for applications. Moreover, it improves the noise robustness.