A new method to determine how occupant characteristics affect fatality risk in traffic crashes is developed. The method, which uses data from the Fatal Accident Reporting System (FARS), focuses on two occupants, a "subject" occupant and an "other" occupant. The probabilities of a fatality to the subject occupant when that occupant has one of two characteristics are compared. The other occupant serves essentially a normalizing, or exposure estimating, role. The method uses only fatality frequency data--no external exposure information is required, and it is relatively free from uncertain assumptions. It has wide applicability; examples of potential applications include investigating car occupant fatality risk as a function of sex, age, alcohol use or motorcyclist fatality risk as a function of helmet use. The first application is to determining the effectiveness of safety belts in preventing car occupant fatalities, as described in the paper following this paper.