The invention relates to an apparatus for making a multilayer composite pipe. The multilayer composite pipe comprises an innermost layer (2) made of plastic. The pipe has a seamless metal layer (4) or a metal layer (4) having an axial, non-overlapping seam. The outer surface of the metal layer is treated for changing its outer appearance. There-after a transparent outermost layer (8) is provided on the outer surface of the metal layer. The structure of the pipe is such that the pipe can be permanently bent to certain angles without significant spring back.