Since the observability for bilinear systems is affected by the input, this paper defines three kinds of observability for bilinear systems ; namely (1) observability with some input, (2) observability with any input, (3) observability with unknown input. The necessary and sufficient condition for the observability with some input and sufficient conditions for the observability with any input and with unknown input for discrete bilinear systems are derived respectively and the effects of the input are clarified