The Walsh system will be investigated in the Kaczmarz rearrangement. In an earlier paper we have shown that the maximal operator of the (C,1)-means of the Walsh–Kaczmarz–Fourier series is bounded from the dyadic Hardy space H p into L p for every 1 2 <p⩽1 . In the present work, we extend this result to the ( C, α) means when 0< α⩽1 and prove their maximal operator σ α : H p → L p is bounded for all 1/( α+1)< p⩽1. By known results on interpolation we get from this theorem that σ α is of weak type (1,1) and bounded from L q into L q if 1< q⩽∞. Moreover, the ( C, α) means of an integrable function f converge to f a.e.