At each application of the recursive process presented below, a set of problems is solved sequentially. A typical problem at each stage of the process comprises an aperture of a certain width in a conducting cylinder. Its solution is constructed from the data available at this stage, viz. the solution for the preceding problem and an additional aperture cut into the conductor. This process complements the add-on patch formulation reported in the recent past, and it retains its useful features. Prior to commencing the process, the short circuited conductor is efficiently analyzed with pulse shaped incident electric fields. The "short circuited" current obtained in this pre-processing stage is used to generate building blocks for the subsequent recursive process. From this point on, only the electric field quantities are used for representing both the exciting and the unknown functions. This representation leads to a purely algebraic algorithm, which requires no integral operators and hence is quite efficient. This method is most suitable for large conductors with smaller aperture, and for cases where the large short circuited conductors are easily computable.