In this paper we applied the Superposition Principle with a new basic conductor voltage condition for the computed electric field in three-core cables and the results obtained have higher accuracy and lower computational time than the previous works. The maximum potential errors is not more than 0.050% and the maximum field deviat8ion angle is not more than 0.011". The electric field problem under arbitrary conductor voltage condition is reduced to a field computation for a new basic conductor voltage condition (O,l,-1) which reduces the computing time because it doesn't require the repetitive solution of the algorithm for different u t values. With this new configuration, it is possible to take advantages of a symmetrical conductor arrangement, reducing the number of charges necessary for the field calculation and the Superposition Principle is applied only two times.