And Edinburgh have not been victorious outside of Scotland in the tournament since they visited Benetton Treviso in September.
Ulster sit top of the pile going into the weekend following a bonus-point victory over Glasgow Warriors thanks to a try from Callum Black in his centenary appearance.
And they face the Scarlets this weekend in a rich vein of form, having gained 22 league points in their last six games.
Scarlets won 22-12 when the sides last met in September in Llanelli and have not achieved a season's double over the Ulstermen since the 2008/2009 season.
Benetton Treviso claimed their first win of the campaign, narrowly beating Cardiff Blues 13-7 at Stadio Monigo, and they face Newport Gwent Dragons who have only tasted victory once in their previous five matches.
Jayden Hayward will have an opportunity to improve on the already impressive four tries and 110 points he has scored in 13 appearances for Treviso this season.
Dragons and Treviso are the only two sides who are yet to win away from home in the 2015/16 campaign, while the Welsh side's only loss against the Italians in their last six meetings was in April 2014.
Glasgow Warriors welcome Munster to Kilmarnock looking to improve on an impressive record they hold against Irish provinces.
The Warriors have won their last nine fixtures against Irish sides, although they have not completed a season's double over Munster since 2011/2012.
Cardiff Blues will look to get back to winning ways after their five-match winning streak came to an end when they visited Treviso on Saturday.
They entertain third-placed Leinster at Adams Park who currently have the best defence in the PRO12 only, conceding 12 tries all season.
The Leinstermen have only won once in their last six visits to Wales, though, last beating Ospreys at Liberty Stadium on January 8.
And Zebre entertain the best attack in the division when they host Connacht at Stadio Sergio Lanfranchi.
The Italian outfit sustained their second heaviest defeat last Saturday when they were on the receiving end of a hefty 55-0 defeat to Leinster at RDS Arena.
The Parma outfit last beat and Irish province side in September 2014, emerging 13-6 winners against Ulster.
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