## (Lobachevskii Journal of Mathematics, Vol.13, pp.39-43)

An $L^{1}$--convergence property of the complex form $g_{n}(c,t)=S_{n}(c,t)- \left[ c_{n}E_{n}(t)+c_{-n}E_{-n}(t) \right]$ of the modified sums introduced by Garrett and Stanojevi\'{c} [3] is established and a necessary and sufficient\ condition for $L^{1}$-convergence of Fourier series is obtained.