The 15-Puzzle

Is it possible to take a standard 15 puzzle (the numbers 1-15 on those sliding tiles, with one blank space) in the starting position:

1234

5678

9ABC

DEF_

and (without taking the pieces out of the puzzle) transpose the pieces so that the puzzle reads

159D

26AE

37BF

48C_

? It it possible to transpose the 3x3 8-piece puzzle in this way?

I know the answer... leave your thoughts in the comments.