ifconfig eth1 hw ether 00:01:02:03:04:05
and I got the following error
SIOCSIFHWADDR: Device or resource busy
Then I tried the following command
ifconfig eth1 down hw ether 00:01:02:03:04:05
and it worked!
I also updated the file /etc/iftab with the new MAC address for eth1. Otherwise the system will be confused after a reboot.