If you're going to be fussy, this is not a frisbee, since it does not involve the famous pie-tins.
It is, however, eminently modifiable, decorateable (is that a word? It is now.), and suitable for using indoors.
Even better, it can be educational (see the last step).
Print one out with your corporate logo, then if you're caught playing with one of these at work, tell them you're using your initiative and testing out a potential marketing tool...
Step 1: The Template
As is my wont, this is made from a single A4 sheet, this time of light cardstock (about 160gsm, if you need to know).
I have included a PDF drawn up from a scan of my original sketch, including two versions - one decorated, one plain and awaiting decoration by your good self.
Print out the one you want, then cut it out, including the seven rectangles at the top.
(If you are going to decorate your frisbee by hand, do so before you cut it out.)