A safety brake for an elevator system having at least one traveling body movable in an elevator shaft along a guide rail and/or a brake rail. The safety brake is suitable for braking and retaining the traveling body on the guide and/or brake rail as required. The safety brake includes a control plate for receiving a brake body and for positioning the brake body relative to the guide and/or brake rail. The brake body is designed in at least two pieces and includes a first brake element and a second brake element. The first brake element is solely for braking and retaining purposes when the traveling body is moving along the guide and/or brake rail in an upward direction, and the second brake element is solely for braking and retaining purposes when the traveling body is moving along the guide and/or the brake rail in a downward direction.