First, try deactivating all plugins before initiating the update.
If that doesn't help, here are three ways to increase PHP's memory allocation:
1. If you can edit or override the system
php.ini file, increase the memory limit. For example,
memory_limit = 256M
2. If you cannot edit or override the system
php.ini file, add
php_value memory_limit 256M to your
3. If neither of these work, it's time to ask your hosting provider to temporarily increase PHP's memory allocation on your account. Keep in mind that most decent hosting providers allocate 32 MB to PHP under each account, and most decent hosting providers allow users to temporarily increase the memory allocation. If your hosting provider won't accommodate you, perhaps it's time to find a new hosting provider.