Smoother grid based movement using coroutines and lerp

Hi. I move my player on the scene using a coroutine and linear interpolation to simulate a grid based movement. Everything works perfectly except one thing: it looks like there's a little gap between the tiles during movement. When the player moves from A to B it stops for a little while, the positions are recalculated and the movement start again. The problem is that on a protractred movement this gap between method calls decrease the whole smoothness of the movement. Is there any solution?