Ah. Thanks NiLuJe. It confused me that it works differently than on Ubuntu.
Code:
[root@kindle us]# ls a
a.txt
[root@kindle us]# ls b
b.txt
[root@kindle us]# mount --bind b a
[root@kindle us]# ls a
b.txt
[root@kindle us]# ls b
b.txt
[root@kindle us]# umount b
umount: b: not mounted
[root@kindle us]# umount a
[root@kindle us]# ls a
a.txt
[root@kindle us]# ls b
b.txt