In 1987 Harris proved [11] -among others-that for each 1 ≤ p < 2 there exists a two-dimensional function f ∈ L p such that its triangular Walsh-Fourier series diverges almost everywhere. In this paper we investigate the Fejér (or (C, 1)) means of the triangle two variable Walsh-Fourier series of L 1 functions. Namely, we prove the a.e. convergence