Their latest opponents the Scarlets, having claimed the scalp of Munster in Cork last weekend, will be anxious to add another Irish province to their tally.
Ulster have already pulled out a six-point lead over the Scarlets at the top of the table, and should this result go their way could see that gap increase into double figures.
The round starts on Friday night with reigning champions the Ospreys facing the Cardiff Blues at the Liberty Stadium.
The visiting Blues will need all their skills if they are to overcome the odds and return with the points, something they have only achieved once on Ospreys soil since the Welsh regions were formed.
The remaining four games are on Saturday, one in Italy and three in Ireland. The Newport Gwent Dragons are the third Welsh region to visit the Stadio di Monigo in Treviso this season, and none of them have come away with a win as of yet.
Zebre make their first visit to the home of current Heineken Cup champions Leinster. The Italian outfit lost by the slimmest of margins the last time they played an Irish province, the rearranged game against Ulster, but the RDS in Dublin will be a very hard place to go in search of a maiden win.
Edinburgh, having beaten the Ospreys last time out, travel to the west of Ireland to face Connacht at the Sportsground. Always a difficult place to visit, Edinburgh have not won in Galway since 2008.
And finally there will be a point to prove at Thomond Park when Munster take on Glasgow Warriors. Both teams were defeated last time out.
Leinster ended the Warriors' hopes of a potential record-breaking winning run, while Munster's home loss to the Scarlets leaves them just outside the play-off zone in fifth spot. So, both teams will be gunning for a victory to get them back on track.
RABODIRECT PRO12 - ROUND 10 FIXTURES:
Friday, November 30 -
Ospreys (6th) v Cardiff Blues (7th), Liberty Stadium, 7.05pm (live BBC 2 Wales)
Saturday, December 1 -
Benetton Treviso (10th) v Newport Gwent Dragons (11th), Stadio di Monigo, 3pm local time (live SportItalia)
CONNACHT (9th) v Edinburgh (8th), the Sportsground, 5pm
LEINSTER (4th) v Zebre (12th), the RDS, 6pm (live RTÉ Two)
MUNSTER (5th) v Glasgow Warriors (3rd), Thomond Park, 7.45pm (live TG4/BBC ALBA)
Sunday, December 2 -
Scarlets (2nd) v ULSTER (1st), Parc y Scarlets, 4pm (live BBC 2 Northern Ireland/RTÉ Two/S4C)