Résumé : Result are presented of an emulsion study of the low energy part of the π+ spectrum (1 MeV < Tπ < 30 MeV) resulting from 4639 τ′ decays of K+ mesons at rest. Contrary to the findings of Davison et al. this experiment shows no evidence for the existence of the σ(π0π0) resonant state, there being no lack of events at the lowest energies. The spectrum is analysed in terms of a standard polynomial development of the decay matrix element. © 1976.