Integration of single-cell multiomics profiles generated by different single-cell technologies from the same biological sample is still challenging. Previous approaches based on shared features have only provided approximate solutions. Here, we present a novel mathematical solution named bi-order canonical correlation analysis (bi-CCA), which extends the widely used CCA approach to iteratively align the rows and the columns between data matrices. Bi-CCA is generally applicable to combinations of any two single-cell modalities. Validations using co-assayed ground truth data and application to a CAR-NK study and a fetal muscle atlas demonstrate its capability in generating accurate multimodal co-embeddings and discovering cellular identity.