An arrangement for transmitting independent serial data streams through synchronous Time Division Multiplexing (TDM) switches with a number of input and output lines is disclosed. At the receivingside of a switch, there is one data buffer per TDM bus buffering the data before transfer on the bus. A connection table associated with each buffer includes entries addressing the bytes in the buffer. The order of the addresses determines the order of the bytes as they are transferred over the bus. Also, at the transmitting side, there is one data buffer per bus, but only one common connection table. The connection table is divided into one memory area per output line, and determines the order of the data bytes, as they will occur at the respective output lines.