With classic models of stars, in which overshooting from convective cores is not taken into account, the transition mass, Mtr, separating stars which undergo core He-flash from stars which ignite He-burning nonviolently in a non degenerate core, is set around 2.2 M⊙ (Iben 1967) for Pop I chemical composition (X = 0.700, Z = 0.020). This value is known however to depend on the chemical abundances, being lower at increasing Y and decreasing Z (Wagner 1974; Sweigart and Gross 1978). However, in recent years many independent arguments have indicated that convective overshooting from the central cores may play an important role in stellar evoluion (Bertelli et al 1985). In order to assess the dependence of Mtr on overshooting, we have computed evolutionary sequences of 1.4 M⊙, 1.5 M⊙ and 1.6 M⊙ with chemical composition X = 0.700 and Z = 0.020 adopting the description of convective overshooting formulated by Bressan et al (1981) for their parameter λ = 1/Hp = 1. As shown in the Tc vs pc diagram of Fig 1, while the tracks of 1.4 M⊙ and 1.5 M⊙ stars deeply penetrate into the region of high degeneracy and likely undergo core He-flah, the 1.6 M⊙ star succeeds in igniting helium in non degenerate conditions. This means that the classic value of 2.2 M⊙ for Mtr is now lowered to the mass range 1.6 to 1.5 M⊙. The HR diagram of the 1.4 M⊙, 1.5 M⊙ and 1.6 M⊙ stars in presence of convective overshooting is shown in Fig 2. The region of stationary core He-burning for the 1.6 M⊙ and the extension of the red giant branches for the 1.4 M⊙ and 1.5 M⊙ stars are also indicated.