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I updated the BIOS of my EeePC 900 using the following howto

http://wiki.debian.org/DebianEeePC/HowTo/UpgradeBIOS

and it is working ok.

I just run the following steps:

1. Download the BIOS image from http://support.asus.com/download/download.aspx or from http://update.eeepc.asus.com/bios/. Make sure you select the right model.
2. Prepare an USB drive formatted with FAT16 filesystem. Note that a SD card won’t work, unless you insert it in an USB card reader. To format it using FAT16, use mkdosfs -F 16 (tip from twb). If you get an error, you may need to run *fdisk on the USB drive and shrink the partition you’re using (16 MB partition seems to work). Yes, it really does have to be FAT16.
3. Open the downloaded file. It should contain a file named like 900-ASUS-0906.ROM. The 900 part corresponds to the EeePC model. Copy that file in the root directory of the USB key, and rename it to 900.ROM. Again, 900 corresponds to the model. If your model is 901, then the download file should contain version.ROM and it should be renamed to 901.ROM when copied on the USB key.
4. Reboot and press Alt+F2 during the boot. The BIOS updating program will start searching for USB drives, then for a suitably named ROM file. Follow the instructions on the screen.

So good work now!

Reference:

http://wiki.debian.org/DebianEeePC/HowTo/UpgradeBIOS