Change black box around a Raster

Using the GDAL Georeferencer QGIS 3.10.10 I have georeferenced an old map, so now it is rotated a bit. The NoData fields for the "frame" are now black (RBG = 0,0,0). I would like to get rid of the frame, but if I turn the RGB-Value of 0, 0, 0 to 100% transparency, some areas of the actual map, which are also black will become totally transparent too.

I vaguely remember solving this problem some years back by loading the georerenced TIFF into GIMP and filling the "frame" with some other colour that is not in my map image and then setting this colour to transparent in QGIS. I tried this this time, but the georeferencing is lost.

Does anyone know, how to remove the black frame without loosing the black pixel of my map?