Pat Lam wants his men to create their own bit of history tomorrow as they continue their quest for a first ever top-six finish in the league.
Connacht have never before defeated the three provinces in the same season but victory over Ulster tomorrow at the Sportsground would change all that.
Lam's men will bid to complete the hat-trick having beaten Leinster 10-9 at the Sportsground in September and followed that up with a 24-16 success over Munster on New Year's Day.
Coach Lam said that it would be a notable achievement for this group of players to defeat all three rival provinces.
"It would be massive for Connacht Rugby and in the context of where Connacht has come from and where they would like to go," he said.
"In my first year last year we won no derby games but to be able to beat Leinster was great and to beat Munster after such a long time was fantastic too, but to be able to do all three is a bit of history.
"And the other thing that was pleasing when we played Munster and Leinster they had a lot of their internationals there. That is the thing that will take a lot of pride on, that we played them pretty close to full strength."
But the task facing Connacht against an Ulster side who are second in the table, just two points off leaders Glasgow, is illustrated by the fact that they have only beaten them once in the last 17 league meetings.
That win came at the Sportsground in April 2012 when tries from Tiernan O'Halloran, Gavin Duffy and Miah Nikora sealed a 26-21 success, but Ulster have won all five games since then.
Connacht's primary target is to make the top six but they are the only team in the league who will play three of the current top four in their remaining games.
Edinburgh, level on points, and Scarlets, three points behind, have easier run-ins. The Scots play two of the current bottom four while Scarlets' remaining games are all against the clubs in the bottom four.
Incidentally, Connacht, with eight yellow cards, are second in the Specsavers Fairplay League, with eight points to Leinster's seven. Ulster are bottom of the table with 26 points, with eight yellow and two red cards, along with four proven citings.