A beverage preparation machine (1) comprises: a beverage preparation module (20, 30) having a front face (21) with an outlet (31) for dispensing a prepared beverage; and a cup support (10) located under the outlet (31) for placing a cup (2) under the outlet (31). The cup support (10) has a rear face (11) removably assembled to the front face (21) by a mechanical connector arrangement (12,22) that comprises a front hook (22) on the front face (21) disassemblable from a corresponding rear hook (12) on the rear face (11). The rear hook (12) has a retaining element (121) and the front hook (22) has a retaining element (221), the retaining elements (121,221) being mutually engaged when the cup support (10) is assembled to the front face (21) and disengaged when the cup support (10) is disassembled from the front face (21). The retaining element (121) of the rear hook (12) extends generally in parallel to the rear face (12) and the retaining element (221) of the front hook (22) extends generally in parallel to the front face (21), so that the rear face (11) and the front face (21) are relatively slid in parallel one over another to move the retaining elements (121,221): together from disengagement into mutual engagement to assemble the rear face (11) to the front face (21); and apart from mutual engagement into disengagement to disassemble the rear face (11) from the front face (21).