Let be a plane graph, and let be a colouring of its edges. The edge colouring of is called facial non-repetitive if for no sequence , , of consecutive edge colours of any facial path we have for all . Assume that each edge of a plane graph is endowed with a list of colours, one of which has to be chosen to colour . The smallest integer such that for every list assignment with minimum list length at least there exists a facial non-repetitive edge colouring of with colours from the associated lists is the facial Thue choice index of , and it is denoted by . In this article we show that for arbitrary plane graphs . Moreover, we give some better bounds for special classes of plane graphs.