Roller blind with conical roller support

The blind has a roller support (31) formed by a band (37), which is wound up for producing a cylindrical sleeve on a core (35) of the roller support. A blind track includes a shape deviating from rectangle and is attached, with an edge, to an outer peripheral surface of the sleeve and a free part of the core. The roller support is an approximate truncated cone, which is approximated with the help of the core and a wrap (38).