The invention relates to a membrane filter for operating while submerged, with a frame (1), which can be lowered into the liquid to be purified, and with modules (2) adjacently arranged in a row. The modules (2) each have a base element (3) with a permeate collecting chamber (4), tubes (5) for a fluid that are connected to both ends of the base element (3), and with hollow fiber membranes (6) that, with an open end, are embedded in the base element (3). The hollow fiber membranes (6) are closed at their other end and terminate inside the liquid to be purified without being fixed whereby being able to freely move. The tubes (5) are vertically oriented and, at the top, are connected to a collecting line. Fiber holding devices (7) for laterally guiding the hollow fiber membrane (6) are fastened to the tubes (5). According to the invention, the fiber holding devices (7) are provided in the form of U-shaped brackets that have a web (8) and limbs (9), which are located at the ends of the web and can be fastened to the tubes (5), and these brackets surround the hollow fiber membranes (6) of a module (2) on one side in the longitudinal direction and, due to a correspondingly large dimensioned limb length, also surround the membranes at the ends in front of the tubes (8).