Craftlady is correct. The same thing worked for us.
Cammie had awful dandruff when we adopted her from the shelter. We didn't bathe her but brushed her very gently every day to get all the dead skin off. Once she adapted to her new food (Science Diet) her dandruff disappeared. At first we bought Nutranugget because it's the food they use at the shelter. We thought it would help her relax if she had familiar food. She wouldn't touch the stuff. Her coat used to be rough and dull but now it is glossy. Some of that could have been due to the stress at the shelter.