"Upgrade patch can not be installed ..." while installing Visual Studio SP1 for Vista

To be able to use Visual Studio 2005 on a Windows Vista machine, you need to install a special service pack: (Visual Studio 2005 Service Pack 1 Update for Windows Vista).

When starting the installation I received the following error:

The upgrade patch cannot be installed by the Windows Installer service because the program to be upgraded may be missing, or the upgrade patch may update a different version of the program. Verify that the program to be upgraded exists on your computer and that you have the correct upgrade patch.

The service pack is searching for specific components that are not available. These components ship with the standard SP1. So before installing the Vista specific service pack, you need to install the standard SP1.