This method of summability, known as harmonic summability, was introduced by Riesz in 1924 [5]. This method is regular [5]. We obtain another method of summation viz., (N, 1/(n+1)). Ci by superimposing the method (N, 1/(n+1)) on the Cesaro means of order one. 1.2. Let f(t) be a function which is integrable in the sense of Lebesgue over the interval (ir, r) and is defined outside this interval by periodicity. Let the Fourier series of f(x) be 1 X 1 X ( . 21)aO + 1:(an cos nx + bn sin nx) aO + A An(x); 2 n1 2 then the conjugate series of (1.21) is