In the field of beverage making devices (10) comprising a brew chamber (23), a rinsing procedure may be applied to a beverage making device (10) for the purpose of rinsing the brew chamber (23) with water prior to or after a beverage brewing process. Measures are taken to achieve that a discharge of rinsing water from the brew chamber (23) takes place at another position on the brew chamber (23) than the position of a beverage outlet (30) of the brew chamber (23). This can be done on the basis of appropriate control of operation of the beverage making device (10) during the rinsing procedure. The brew chamber (23) does not need to have a separate rinsing water outlet, as use may be made of a water inlet (33) of the brew chamber (23) for the purpose of discharging the rinsing water from the brew chamber (23), for example.