Tile based movement in flash as3

Hello i am currently working on the engine for a tiled based game. I have set up the map using a 2 dimensional array. Movement wise i have just increased/decreased the x/y position of my characer by the same amount of pixels as my tiles. Anyway of course this does not look good as my character is just "teleporting" to the next tile. Perhaps anyone can help me how to make some smooth movement and still ensure that my character will end up in the middle of a tile (Just like in the pokemon games).

Any help is much appreciated - John