Yes, you can make your next batch of yoghurt from a previous yoghurt. This is known as cloning or back slopping.
Be aware that when cloning from a previous batch, you are cloning all of the bacteria present in the yoghurt including any contaminants that may have blown in through the window or any you may have accidentally introduced yourself
It may be considered a false economy, risking the disappointment of failed yoghurt to save 25 cents worth of culture.
It is also typical that the second and third generations of even successfully cloned yoghurt tend to produce a weaker thinner curd, as while there may be no bad contaminants present there will be more growing in your yoghurt than just the yoghurt bacteria. These extra bacteria start competing with the yoghurt bacteria that make flavour and texture.