Holders Celtic have been drawn at home to Hearts in the quarter-finals of the Co-operative Insurance Cup.
Dundee, the only non-Scottish Premier League survivors, host Scottish champions Rangers after the draw was made at Hampden Park on Thursday.
The Dark Blues knocked out SPL side Aberdeen in the third round on Tuesday.
St Johnstone host a Tayside derby, with Dundee United making the short trip to Perth, while Motherwell travel to Paisley to take on St Mirren.
The tie at Celtic Park will be shown live on television by BBC Scotland, with a 1935 GMT kick off on Wednesday 28 October.
Hearts manager Csaba Laszlo will hope to avoid the last-minute misery his side suffered in Saturday's league visit to the Glasgow ground, where they lost 2-1 with the final action of the match.
"Sometimes it is easier to play against a team like Celtic because you do not require any extra motivation"
"It's a different type of game, because cup games have their own rules," he told his club website.
"But we must go with confidence and try to get to the next round.
"It does not matter if we are at home or away.
"Everything is possible. Sometimes it is easier to play against a team like Celtic because you do not require any extra motivation.
"Celtic being favourites possibly makes it easier for us, but we will go for the victory."
Co-operative Insurance Cup fourth-round draw
Celtic v Hearts
Dundee v Rangers
St Johnstone v Dundee United
St Mirren v Motherwell
The ties will be played in the week commencing 26 October.
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