Vacuum-remelted-type 316L stainless steel is oxidized in air at 100°C and 250°C baked in vacuum. This oxidation and baking produce a surface in an extremely low outgassing state, as low as 4×10-11 Pam3/sm2. The temperature of baking following the atmospheric oxidation should be equal to or higher than the temperature of oxidation to produce a lower outgassing state compared to the corresponding fully degassed state without oxidation. The oxidation reduces C contaminants present on the surface and the quantity of desorbable CO, which may lead to the reduction of CO outgassing from the surface. Further, the surface oxide layer formed by the atmospheric oxidation is 57 nm thick and appears to effectively retard hydrogen diffusion from the bulk.