Ulster moved off the bottom of the Magners League table last Friday by recording their first win since September and their first away win since April.
Caretaker coach Williams has no injury worries following the victory over Connacht in Galway and the Welshman has selected an extended squad for Friday's clash with Edinburgh.
Looking ahead to the game, Ulster hooker and captain Rory Best said: "Friday night is now the biggest game of our season again, like Friday past was and the week after will be. We can't go looking beyond Edinburgh."
Former Ulster winger Andrew Maxwell, who scored an excellent individual try for Edinburgh in their defeat of Llanelli last Sunday, is looking forward to facing his old club.
He said: "The thing with Ulster is to get on top of them and play at your pace, and don't let them control the game, which they're good at. They won on Friday night and will be looking to get some momentum going now. It's a massive match for both teams."
Ulster Rugby have put two ticket offers in place for this fixture including a limited number of terrace tickets available online for just Â£10 and special youth group offers.
The terrace ticket offer has been extended due to high demand and there are still group offers available for the fixture.
Tickets can be purchased online from www.UlsterRugby.com and the Ulster Rugby ticket line (tel: 028 9049 3222 (Option 2)) between 10am-12pm or alternatively from over the Ravenhill counter.
Tickets can also be bought from various ticket outlet shops across the province, which are listed on the Ulster Rugby website in the ticket section.
ULSTER Squad (v Edinburgh): Backs (13) - Mark Bartholomeusz, Bryn Cunningham, Tommy Bowe, Andrew Trimble, Mark McCrea, Paul Steinmetz, Simon Danielli, Paddy Wallace, Isaac Boss, Paul Marshall, Kieran Campbell, Niall O'Connor, Rob Dewey
Forwards (14) - Justin Fitzpatrick, Rory Best (capt), Nigel Brady, Bryan Young, Stuart Philpott, Tom Court, Matt McCullough, Carlo Del Fava, Neil Best, Kieron Dawson, Roger Wilson, Declan Fitzpatrick, Ryan Caldwell, David Pollock.