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If you don’t fancy upgrading Magento 1 through command line, you can upgrade Magneto core using Magento’s in-built Magento Connect Downloader.
If you login and don’t see any packages, this may be due to the way the site was built.
At the top of Magento connect downloader enter
magento-core/Mage_All_Latest in the in put box, this will install all latest MagentoConnect core packages on top of existing files and will allow future upgrades through Magento Connect Downloader.