Short of trying to upgrade via a new install and going through all the work of transferring your themes etc you can do it via ssh
The following worked for me: (Remember if you are running on a machine with low resources and you have many products the script will take longer to run)
rm -rf var/cache var/session chmod 550 ./mage ./mage mage-setup . ./mage config-set preferred_state stable ./mage list-installed ./mage list-upgrades ./mage install http://connect20.magentocommerce.com/community Mage_All_Latest --force php shell/indexer.php reindexall
As always, your best resource for Magento information is the Magento site
You can access the 1.6 upgrade boards here
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