White Rabbit (WR) is a deterministic Ethernet-based network for general-purpose data transfer and sub-nanosecond time synchronization in large distributed systems. WR has been used in Large Hadron Collider and Large High-Altitude Air Shower Observatory for physics experiment. WR mainly uses the optical fiber for data transmission between WR devices. Commercial off-the-shelf Direct Attach Cable is not suitable for WR network at 100 m level distance. Considering the lower cost of Category (CAT) Ethernet cable compared to optical fiber and the demand of remote power supply in distributed system at 100 m level length, we developed a novel transmission scheme with CAT Ethernet cable for WR. The novel transmission scheme uses the CAT Ethernet cable and small form-factor pluggable connector which is compatible with the optical links. This scheme only uses two pairs of twisted lines in the CAT Ethernet cable for data uplink and downlink. The other two pairs of twisted lines are used for remote power supply. The novel transmission scheme could use the CAT Ethernet cable to complete remote power supply and time synchronization with expected time offset of less than 100 ps and standard deviation of less than 20 ps in the WR distributed system. The distance of distributed nodes could be 80 m with one CAT 7 Ethernet cable or 150 m with relay transceiver connecting two CAT 7 Ethernet cables. In the short-distance scenarios, the novel transmission scheme has lower cost than the optical fiber and additional power supply function.