Small-scale statistics of wavelet-based quantities of turbulence are examined, with particular attention to t α,β[ ι ], which is the wavelet-based transfer of the wavelet-based energy e α[ ι ] at location ι and scale r α to all scales smaller than r β (⩽r α). A divergence-free orthonormal wavelet decomposition method is applied to direct numerical simulation data of three-dimensional incompressible homogeneous isotropic turbulence with grid points and Taylor microscale Reynolds numbers up to 20483 and 732, respectively. We propose a new statistical measure for the degree of scale locality of wavelet-based energy flux to scales smaller than r β constructed from t α,β[ ι ]. At R λ = 732, the measure retains a constant value in the inertial subrange, a value about two-thirds as large as that in the dissipation range, though the flux is local in scale throughout the range, from the inertial subrange to the dissipation range. We confirm that the influence of energy transfer from the large-scale flow on the flu...