||In this Rapid Communication, we study the behavior of a strongly diffusive passive scalar field T submitted to a freely decaying, homogeneous and isotropic turbulence with eddy-damped quasinormal Markovian simulations. We present a new subrange located between the k−17/3 inertial-diffusive subrange and the Kolmogorov wave number kη. This subrange is generated by small-scale convection linked to kη that balances diffusion effects. Thus, we build a typical length scale k−1CD based on convection and diffusion and give an expression for the shape of the passive scalar spectrum in this subrange ET∼Pr−−−−√k−11/3 using physical arguments. This result unifies two different theories coming from Batchelor [G. K. Batchelor, J. Fluid. Mech. 5, 113 (1959)] and Chasnov [J. Chasnov et al., Phys. Fluids A 1, 1698 (1989)] and explains results previously obtained experimentally.