A generally cylindrical yarn package having multiple yarn ends is formed by converging the multiple yarn ends to form a substantially planar yarn end ribbon having the multiple yarn ends in a side-by-side untwisted contacting relationship with one another. The yarn end ribbon formed of the converged yarn ends is then wound about a continuously rotating yarn package core by reciprocally traversing the yarn end ribbon parallel to the longitudinal axis of the yarn package core while maintaining the side-by-side untwisted contacting relationship between the multiple yarn ends of the yarn end ribbon. In such a manner, a generally cylindrical yarn package is formed having multiple yarn ends which may later be separated into individual yarn ends for downstream processing by tangentially unwinding and separating the individual yarn ends from the yarn package. As a result, the present invention allows an increase in spinning capacity to be achieved (i.e., since a greater number of yarn ends may be produced) without the need for additional substantial capital investment for new individual winders.