PURPOSE: To obtain a high workability pipe free from the generation of working strains caused by pipe making even without executing finish annealing by controlling the componental compsn. of a Cr-contg. steel, hot rolled sheet annealing conditions and cooling conditions in specified ranges.

CONSTITUTION: The compsn. of a steel is constituted of, by weight, ≤0.03% C, ≤0.03% N, ≤2% Si, ≤2% Mn, 1 to 40% Cr, and the balance Fe with inevitable impurities. The hot rolled sheet of the same Cr-contg. steel is annealed at 800 to 1100°C and is thereafter cooled between 800 to 500°C at 5 to 80°C/sec cooling rate. Moreover, it is pickled and is thereafter subjected to cold rolling at 5 to 30% cold draft to form into a pipe. Next, it is subjected to short time annealing at 800 to 1100°C for ≤20min and is subjected to recrystallization and stress relieving. This steel compsn. is incorporated with at least one kind among Nb, Ti, Zr and V by ≤1%, and also, the conditions of (Nb/93)+(Ti/48)+(Zr/91)+(V/51)>(C/12)+(N/14) are preferably satisfied.