In a small bowl, mix 125 ml (1/2 cup) of the mixture with the yogurt culture. Pour into the saucepan while stirring. Pass the mixture through a strainer over the yogurt maker tank (see note). Close the yogurt maker. Let ferment for 5 hours at room temperature.
Over a large bowl, place a large fine strainer lined with a layer of paper towels. Pour the yogurt into the strainer. Cover with plastic wrap and let drain in the refrigerator for 4 hours or until the yogurt is completely cool. Discard the liquid. Transfer yogurt to an airtight container.
Homemade Greek yogurt keeps for 2 weeks in the refrigerator.
