To use this method widely for the transmission of a high bit rate data by providing a means scheduling an ATM cell transmission time and a means multiplexing a plurality of low bit rate connections into the same ATM connection having a scheduled ATM cell transmission time.

A multiplexing means 8 maps a selected octet into an ATM cell such as an ATMn as shown by 40 or 41. The means 8 further decides so as to maintain a new AST and an ATM cell interval as constant as possible regardless of the kind of a case of lists LL0 and LL1 to be linked in each of scheduled ATM cell transmission time ASTs. Then, the means 8 schedules an ATM cell transmission cell transmission time in the form of maintaining the ATM cell interval as constant as possible and multiplexes a plurality of low bit rate connections into the same ATM connection having the scheduled ATM cell transmission time.