Simulate random iteration of array

I have an array of given size. I want to traverse it is pseudorandom order, keeping array intact. It will be best if current state can be stored in a few integers.

I know you can't have full randomness without storing full array, but I don't need the order to be really random. I need it to be perceived as random by user.

One possible suggestion - using large prime number - is given here. The problem with this solution is that there is an obvious fixed step (taken module array size). I would prefer a solution which is not so obviously non-random. Is there a better solution?