We predict a new type of negative differential resistance (NDR) in a nonlinear ten-junction array of nine conducting islands with ultrasmall self-capacitance. A main feature of our array is that two of the ten junctions go in the direction opposite to an external in-plane electric field. The NDR characteristic is one of Coulomb blockade phenomena and is triggered by competition between the two tunnel rates across two specific junctions depending on the external voltage. Calculations for the electron dynamics are based on the orthodox semiclassical single electron tunneling model.