We introduce a new row insertion algorithm on increasing tableaux and decreasing tableaux, generalizing Edelman-Greene (EG) row insertion. Our row insertion algorithm is a nontrivial variation of Hecke column insertion which generalizes EG column insertion. Similar to the Hecke column insertion, our row insertion is bijective and respects Hecke equivalence. Therefore, it can recover some applications of the Hecke column insertion. In future work, we will apply this insertion to establish several results that cannot be done by the Hecke column insertion.
