Coordinate the animator with the clip's filp

Question

I make my character turn on himself. To save money I only have the sprites where he looks left and not right. I flip the animation so that he looks to the right.

To activate the action look left I change the Integer in the animator that defines the orientation. And for the filp I do it on the spriteRenderer. My problem is that the 2 are not done at the same time, so between the moment he looks right and left, he looks in front and at a moment the front image is flipped before he looks right, it makes an absolutely horrible effect in my game.

How do I get the flip to happen at the exact same time as the animation changes?

IEnumerator updateOrientation()
{
    yield return new WaitForEndOfFrame();

    int orientationAnimation;
    if(angle<45 && angle>=-45)
    {
        orientationAnimation=FACE; //"face";
        orientationActuelle="face";
        spriteRenderer.flipX=false;
    }
    else if(angle<-45)
    {
        orientationAnimation=LEFT; //"right";
        orientationActuelle="right";
        spriteRenderer.flipX=true;
    }
    else if(angle>=45)
    {
        orientationAnimation=LEFT; //"left";
        orientationActuelle="left";
        spriteRenderer.flipX=false;
    }

    animator.SetInteger("orientation_animation",orientationAnimation);

    yield break;
}