The present invention relates to a float process for manufacturing glass sheets, in which molten glass is poured onto a liquid support denser than the glass and then the continuous ribbon which forms is advanced toward the downstream end, this process being characterized in that the thickened edges of the ribbon are trimmed continuously in the forming zone. This process makes it possible to obtain thin glass sheets, such as sheets of film glass, with good flatness, particularly in small plants. The invention also relates to a plant for implementing the process and to the products obtained. FIG. 1.