A new method is employed to measure the neutral current cross section up to Bjorken-x values of one with the ZEUS detector at HERA using an integrated luminosity of 187 pb^-1 of e-p collisions at sqrt(s) = 318 GeV. Cross sections have been extracted for Q^2 >= 575 GeV^2. A much improved precision with respect to the previous ZEUS publication, which only used 16.7 pb^-1 of e-p collisions, is achieved, owing to the larger data sample and improved kinematic reconstruction methods. The measurement is well described by predictions based on the CTEQ6D PDFs.