This study focuses on the design of orthogonal operators based on unique Electroencephalograph (EEG) signal decompositions in order to detect interictal spikes that characterize epileptic seizures in EEG data. The merits of the algorithm are: (a) in elaborating a unique analysis scheme that scrutinizes EEG data through orthogonal operators designed to extract features that best characterize spikes in epileptogenic EEG data; and (b) in establishing mathematical derivations that provide quantitative measures through the designed operators, and characterize and locate the event of an interictal spike. The uniqueness of this algorithm is in its good performance and simplicity of implementation. Clinical experiments involved 31 patients with focal epilepsy. EEG data collected from 10 of these patients were used initially in a training phase to ascertain the reliability of the observable and formulated features that were used in the spike detection process. Spikes were annotated independently by three EEG experts. On evaluation of the algorithm using the 21 remaining patients in the testing phase revealed a Precision (Positive Predictive Value) of 92% and a Sensitivity of 82%. Based on the 20 to 30-minute epochs of continuous EEG recording per subject, the false detection (FD) rate is estimated at 1.8 FD per hour of recorded EEG. These are good results that support further development of this algorithm for EEG diagnosis.