A new, systematic method of generating orthogonal sets of sequences with good correlation properties is described. An orthogonal set is defined as a collection of n sequences, of length n chips, that are mutually orthogonal. Although there are many possible combinations of sequences forming orthogonal sets of a specified length, few have been identified with a structured method of generation such as Walsh codes and orthogonal Gold codes. The application of the new sequences discussed is orthogonal spreading codes in a synchronous code division multiple access (CDMA) system and their correlation properties are considered accordingly.