In 1987 Harris proved (Proc. Amer. Math. Soc., 101) - among others- that for
each 1≤p<2 there exists a two-dimensional function f∈Lp such that
its triangular Walsh-Fourier series diverges almost everywhere. In this paper
we investigate the Fej\'er (or (C,1)) means of the triangle two variable
Walsh-Fourier series of L1 functions. Namely, we prove the a.e. convergence
σn△f=n1∑k=0n−1Sk,n−kf→f
(n→∞) for each integrable two-variable function f