The present invention relates to a process for the manufacture of a frozen dessert, comprising the successive steps consisting in: (a) freezing a mixture containing a fruit puree and/or juice, yoghurt and optionally added sugars and/or other ingredients, in order to obtain a frozen composition, (b) optionally bringing the said frozen composition to a core temperature ranging from -15 to -25°C or from -15 to -30°C, (c) placing the said frozen composition in a device equipped with grinding means and optionally with aerating means, which device does not comprise extrusion means, and (d) texturing the said frozen composition with the aid of the said grinding and optionally aerating means. It also relates to the frozen dessert thus obtained.