A method of installing flooring and resulting structure are disclosed. The method is particularly useful for sanitary nonslip applications such as kitchens. The method includes the steps of positioning a first sheet of polymer flooring material with an upwardly-facing step cut along one edge of the first sheet on a floor to be covered, and applying a second sheet of polymer flooring material with a complementary downwardly-facing step cut along one edge of the second sheet to the upwardly facing step cut of the first sheet and to the floor adjacent the first sheet while concurrently sealing the respective faces to one another in a step lap joint.