To prevent the tip of a tool from being broken or chipped even if heavy cutting such as large feed or large depth of cut is intermittently performed by making the mean thickness of aluminum oxiside multi-layers a specified value.

This alloy comprises Al2O3 multi-layers comprising at least two alternately laminated layers of a Al2O3 unit layer which is 0.5 to 3μm is mean thickness and contains S of 0.1 to 0.2atom% and a pure Al2O3 unit layer which is 0.1 to 1μm in mean thickness and does not contain S substantially. The mean thickness of the Al2O3 multi-layers is 1 to 10μm. When the mean thickness of the Al2O3 multi-layers is over 10μm, the tip of the tool is apt to be broken or chipped.