This gets a bit complicated. Use a copy of your document!

Go into the header for the page you want deleted, that is in a separate section.
Unlink that header from the previous section.
Then, go to the header for the next section, and unlink that one as well.
Then go back to the header you want to delete and delete it.

Header/Footer Settings Recap

You may want to use the following:
Word Toolkit for Advanced Management of Headers and Footers