Is there any way to increase the / partition space without LVM. I am using RHEL 4.

Yes
You can increase the size of the root partition then resize the file system.
Lets assume you have a disk with 3 patitions on it /boot (1) / (2) and /home (3). Ok now lets assume you've moved /home (3)to another disk, you can remove that partition in fdisk and then edit the partition (expert mode) for / (2). You would change the end of the partition to the end of the disk.
finally resize the "/" partition (resize2fs).
Of course remember the most important part is a good tested working backup(s)!
Also I would ensure that you do a fsck of all filessystems first and also this would need to be done from a livecd of some sort of rescue disk.

Hi,

In order to resize partitions without reinstall everything,
I would suggest using GParted http://gparted.sourceforge.net/livecd.php
using that LiveCD you can resize your partitions according to
your needs.

(Please have a backup before doing anything...)

Best regards,