Root Motion Changes Transform pivot position

I have a character model that uses root motion for movement. When moving forward, the pivot of the character's transform moves slight to the left and right (or on the x axis). For example, when idling, the character's position is (0,0,0). When taking the first step, I would like the new position to be (0,0, some distance forward), but what I got is this: Similarly, when taking the next steps, the transform shifts to the opposite direction a little bit: This extra movement becomes a problem for third person camera, because the camera follows the character's pivot, and it will slide on the x axis with the character. Is there a way to eliminate this extra movement or make the camera not affected by that?

I have tried bake in pose and change the animation clips (to remove x axis curves), but the extra movement still exists.