Someone told me that Jadrolinija is operating ferries in Croatia. However, their site is somehow confusing.
Is there any other site with ferry timetables, or specifically, timetables of the Split - Supetar ferry?
I am from Croatia and I find their site confusing as well.
Maybe this link can help you.
IMHO, on this link you have very clear timetable for selected date if that is what you want to find
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On this page, after selecting the English language, you can easily find all the schedule between Split and Supetar (and other cities).
As I've understood, these ferries are quite easy to use - they are frequent (near once in 2 hours) and fast (near 50 minutes to go).