In this paper, we derive the maximal subspace of natural numbers nk: k≥ 0 , such that the restricted maximal operator, defined by supk∈N|σnkF| on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space H1 / 2 to the Lebesgue space L1 / 2. The sharpness of this result is also proved.