Indeed the reigning European champions have lost just three games in the PRO12 this season, to the Ospreys twice and once to Glasgow Warriors in September.
A top of the table finish and a home semi-final are already in the bag but Leinster fans have seen the team lose in the domestic Grand Final for the last two years running and Schmidt is adamant they must go all the way this season.
But first there is the small matter of a Heineken Cup semi-final against Clermont Auvergne at the Stade Chaban-Delmas in Bordeaux next Sunday.
"That's the clean sweep (of six wins against Irish provinces) and is a little achievement that we can store away," said Schmidt.
"Now it's about chasing silverware and it's a hell of a tough task that awaits us next week, and I think both teams (Leinster and Ulster) were looking ahead a little to next week."
Ulster also have a Heineken Cup semi-final against Edinburgh on Saturday and Schmidt leant his support to Brian McLaughlin's team and believes the lack of injured players both teams are carrying stands them in good stead.
"We came through and it looks like they did as well, so that's great Irish news really," added Schmidt.
"Both teams will be able to be reasonably full strength next weekend."
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