How to make divided difference table using cubic hermite interpolation

I have an assignment where I am to interpolate a function on some interval using cubic hermite interpolation. Here is the kicker, I can't use PCHIP. So I must then break my interval into a series of subintervals, to make a bunch of piecwise polynomials, and put them togather using mkpp. So I need to know if anyone has an idea on how to make a divided difference table for cubic hermite interpolation?