Higher-order vortices (HOVs) extend the dimensions of optical vortex regulation, which is of great significance in optical communication and optical tweezers. Herein, we demonstrate an alternative scheme to produce a HOV in the focus plane using multiple Laguerre-Gaussian (LG) beam interference, termed a discrete higher-order optical vortex lattice (DHOVL). The modulation depth of the DHOVL exceeds 2π. In this case, the topological charge (TC) of the DHOVL is determined by the difference of the phase period between the innermost and the outermost interference beams. Compared with a conventional HOV (CHOV), the vortex exists in a form of multiple unit singularities sharing a dark core. In addition, the average orbital angular momentum per photon of the DHOVL increases with increasing TC, surpassing that of the CHOV. This work provides a novel, to the best of our knowledge, scheme to produce a HOV, which will facilitate several advanced applications, including optical micromanipulation, optical sensing and imaging, and optical fabrication.