Celtic start their Champions League qualifying campaign against a team with a worldwide reputation - for their goal celebrations rather than their skills.
Celtic coach John Kennedy is aware that Stjarnan are perhaps not the force they were when Iceland's champions defeated Motherwell last year.
"We will make sure we're well prepared for that," he told BBC Scotland.
"We'll certainly not be disrespectful and make sure we are prepared as well as we can."
Stjarnan won the Icelandic title for the first time last year, but they are best known for their team's choreographed routines, such as landing a fish, a human bicycle and a Rambo shooting spree, which have proved popular in video form around the world.
They also defeated Motherwell 5-4 on aggregate in Europa League qualifying and then knocked out Lech Poznan of Poland.
Stjarnan were denied a place in the group stage by Inter Milan, who later knocked Celtic out in the last 32, with the Italians delivering a 9-0 hammering on aggregate.
Celtic have recent experience of Icelandic football, beating KR Reykjavik in the Champions League qualifiers last season.
"That will be something that stands us in good stead," he said. "We've been to Iceland and know what the standard is there.
"Obviously they had a game against Motherwell last year as well, so we are aware of them and it is a good tie for us as it is not too far to travel and it is familiar territory."
The Urvalsdeild is already nine games into its new season and Stjarnan are in sixth place, eight points adrift of Hafnarfjordur but with a game in hand.
Runar Pall Sigmundsson's side will travel to Glasgow for the first leg of the second qualifying round on 14/15 July, with Celtic heading for Iceland a week later.
Based in Garoabaer, a town near the capital, Reykjavik, in the southwest region of Iceland with a population of 14,000 in the shadow of the Snæfellsjökull glacier, Stjarnan play in the 1,000-capacity Samsungvollur.
The best-known member of the Stjarnan squad is Faroe Islands goalkeeper Gunnar Nielsen, who left Motherwell in March after playing 23 times in two years at Fir Park and previously played for Blackburn Rovers, Manchester City, Wrexham and Tranmere Rovers.
Two veteran former Iceland forwards, Gardar Johannsson and Veigar Pall Gunnarsson, will be known to Celtic manager Ronny Deila as they both number his previous club, Stromsgodset, among their ex employers.
Forward Olafur Karl Finsen has appeared more recently for the national team, while full-backs Johann Laxdal and Hordur Arnason have both made one appearance for their country.
Midfielder Pablo Oshan Battuto Punyed is an El Salvador international.
Kennedy recognises that Celtic, who were seeded for the draw, will be strong favourites to progress and believes they are better prepared than they were last season, when they missed out on the group stage after losing to both Legia Warsaw and Maribor.
"I think there were a lot of changes going on behind the scenes last year and obviously, with the management coming in, and a change in the style of play and it was difficult for the players," he added.
"We failed at the time and we've learned from that and we're much better prepared."
Kennedy does not expect many additions to the Celtic squad.
"We did our business early by bringing Dedryck Boyata from Manchester City," he added. "If we do add, it wouldn't be many.
"We don't have to rush out signing players just for the sake of it."