Cheese curd suitable for conversion into natural hard cheese is prepared by ultrafiltering and diafiltering milk or a milk product to produce a retentate, ripening the retentate by fermenting with a cheese starter culture, coagulating the retentate to produce a coagulum, cutting, cooking and agitating the cut coagulum to produce curd, and separating the curd from whey. The retentate has a concentration Factor of 2-8 and contains 1.0-6.2% w/w lactose. Ripening the retentate produces a pH drop of 0.05-1.5 units. Cutting the a coagulum is at a time between 120% and 220% of coagulation time and cooking is at a temperature of 30.degree.-50.degree. C. Combined cooking and agitating operations take 20-120 minutes. Coagulation may be continuous, and a minor portion of the retentate may be separated, fermented with a cheese starter culture and mixed with the remaining retentate to produce a ripened retentate having a pH of 0.05-1.0 units lower than before ripening.