A member with alumina-based hard coating formed there-on wherein said hard coating contains nitrogen and has a composition represented by the formula (1) below:Al1-xMx(O1-yNy)z (1)(0≦x≦0.5, 0<y≦0.5, z>0)where, M denotes at least one species of elements selected from those belonging to Group 4, Group 5, and Group 6 (excluding Cr), and such elements as Y, Mg, Si, and B.