The neutral current e(+/-)p cross section has been measured up to values of Bjorken x congruent to 1 with the ZEUS detector at HERA using an integrated luminosity of 187 pb(-1) of e(-p) and 142 pb(-1) of e(+)p collisions at root s = 318 GeV. Differential cross sections in x and Q(2), the exchanged boson virtuality, are presented for Q2 >= 725 GeV2. An improved reconstruction method and greatly increased amount of data allows a finer binning in the high-x region of the neutral current cross section and leads to a measurement with much improved precision compared to a similar earlier analysis. The measurements are compared to Standard Model expectations based on a variety of recent parton distribution functions.