Yes. The people of the nation all vote for the person they want to be their leader, who serves for a limited number of years and then steps down, and at that point they choose a new leader. Usually, there is no relation to a prior leader, at least not by blood.

It is a very common system of governance where I come from! There are still some monarchies, but they are rare and largely ceremonial. For instance, Japan still has an Emperor, but the day-to-day running of the nation is done by parliament and the Prime Minister.