The Brams–Taylor–Zwicker procedure is a protocol for envy-free cake-cutting among 4 partners.
That procedure allows two partners to divide an entire cake to
Partner #3 trims one piece to create a two-way tie for the largest; the partners now choose pieces in reverse order (#4, #3, #2, #1).
This creates an envy-free division for the entire cake less the trimmings (This is similar to the Selfridge–Conway discrete procedure).
We use Austin's procedure again with the trimmings and partners #4 and #1, to create 4 pieces each of which equals exactly 1/4 for both of them.
Austin's procedure requires 2 cuts to divide a cake between 2 people with an exact value of 1/2; each of these pieces should be divided with 2 more cuts to generate the 4 pieces with exact value of 1/4.