Languages A, B ∈ NP-complete such that A⋃B = Σ*

I’m pretty new to complexity theory and it seems like I stuck with this problem. We should find language $ B$ such that it accepts any words rejected by $ A$ but in that case, it seems that $ B$ is a complement of $ A$ and therefore $ B$ belongs to $ coNPC$ . What is my mistake? Thank you!