Abstract: A method of and an arrangement for installing a rear-facing child car seat (1) employing a supporting arm (5), mounted on the child seat, which is folded into pressing engagement with the backrest part (13) of the passenger seat. Prior to this, engagement means (33) on the child seat has been caused to engage with fastening means (23) in the car in the transition area between the backrest (13) and the seat (9) of the passenger seat. In a preferred embodiment, the fastening means has a cable loop and the engagement means has a hook means coacting with the loop. For after-tightening of the engagement, there are special after-tightening means (17), which forcibly increases the folding of the supporting arm and/or achieves a retraction of the engagement means (33) for further tightening of the engagement with the fastening means (23).