To make it possible to maintain a brazed layer having ductility by preventing alloying of Cu and Ni.

This stainless steel pipe is made by plastic-deforming the hoop material composed of a stainless steel sheet with brazing filler metal applied on its surface into a pipe, and melting the brazing fiber metal between the walls of the multi-wound pipe, and then cooling the molten brazing filler metal. In this case, the surface is Ni-plated, and a Fe layer is formed on the Ni-plating, and the stainless steel sheet, wherein Cu-plating is applied on the Fe layer, is used as the hoop material, and the Ni layer, Fe layer, and Cu layer existing between the walls of the multi-wound pipe are diffused and spliced.