Two young men attempt to climb to the top of the Vienna Town Hall. One of them, a professional climber, mysteriously loses his grip and dies in a fall.
The Vienna Murder Squad are called in when it becomes apparent that the dead man's body contains traces of a poison which would have paralysed his muscles. When a further murder attempt is made against another climber Niki and Marc realise that they are dealing with a madman.
In between investigating this murder Rex and Marc discover that Rex has to undergo a vigorous test to reassess his abilities as a police dog; they discover that the Sergeant in charge has built a formidable obstacle course which no normal dog would ever get through.