Many thanks to all for the answers but the mystery still remains.
Definitely not a Rigi and I don't think it a Romic headbudges don't match.
Mine has a hoop from laurels and an R inside it. The laurel design has an Italian flag also.
That make things more complicated!
I'm afraid that I face the work of a ghost bike company!
I hope when the color is being removed the frame may tell me its secrets.
Until then any suggestions are more than welcome!