Olympus 35 can be cocked multiple times without firing

First time owning a Oly 35 SP (after a few times testing my friend's), and found a quirk: the camera can be cocked multiple times without firing the shutter. And frame counter increases as it goes. E.g if I start at frame counter 2, and cock the camera 5 times, it will show 7. This is done without film loaded. I assume this is not a normal behavior, yes?

Such cameras contain an interlock between shutter and film-advance to prevent missed exposures. Evidently, yours is stuck or broken. You can work around this problem by always advancing film immediately after each shot. Then you won't wonder whether the film was advanced when you're about to take another photo.