The sentence at the top of the GPL, "...changing it is not allowed," does not give you permission to make a derived license from the text of the GPL.
However, the FSF's GPL FAQ item on modifying the GPL does give you that permission (emphasis mine):
Can I modify the GPL and make a modified license?
It is possible to make modified versions of the GPL, but it tends to have practical consequences.
You can legally use the GPL terms (possibly modified) in another license provided that you call your license by another name and do not include the GPL preamble, and provided you modify the instructions-for-use at the end enough to make it clearly different in wording and not mention GNU (though the actual procedure you describe may be similar).
If you want to use our preamble in a modified license, please write to <email@example.com> for permission. For this purpose we would want to check the actual license requirements to see if we approve of them.
Although we will not raise legal objections to your making a modified license in this way, we hope you will think twice and not do it...
It appears that the FSF (who is the author of the GPL) is explicitly allowing you to make and redistribute a derivative version of the GNU GPL, provided you:
- change the name of the license
- not reuse any part of the GPL preamble (this requires separate specific permission)
- remove mentions of GNU that appear in the how-to-use instructions
That said, the FSF advises that you make use of the license's capability for exceptions instead of writing your own. That will allow you to make the license more permissive but also enjoy the legally-vetted and GPL-compatible verbatim text of the license:
Such a modified license is almost certainly incompatible with the GNU GPL, and that incompatibility blocks useful combinations of modules. The mere proliferation of different free software licenses is a burden in and of itself.
Rather than modifying the GPL, please use the exception mechanism offered by GPL version 3.
For more information about GPL exceptions, see the FAQ: