A method and control device for controlling the display of multimedia data on an audio-video rendering device, e.g. a TV device (AVD), when a channel change action, from a first channel to a second channel, is activated. It is controlled which, how and when particular multimedia data is displayed as it may for instance be necessary to perform parental control to prevent the display of "adult" multimedia data at particular times of the day, or advertisements at times when they could disturb the comfort of watching of the user of the TV set. To improve program search efficiency during the channel change action for allowing a user to effectively and pleasantly look for and discover programs to watch, the embodiment comprises a remote control unit command receiver (RCUCR) to intercept actions of a remote control unit (RCU), a trick play command analyzer (TPCA) to analyze whether the intercepted action consists in activating a channel change action, a search/discovery mode detector (SDMD) to interpret the type of multimedia data transmitted on the second channel if a channel change action was activated, and a multimedia data type controller (ADIF) to prevent the multimedia data of the second channel to be displayed on the TV device (AVD) if this multimedia data is of a predetermined type, e.g. advertisements (ADS). In a preferred embodiment, multimedia data of a second type, e.g. "normal" programs (PGS) or previews of programs (PRS) is displayed in replacement of the advertisements during a predetermined time delay called advertisement-play grace period.