use of the kernel and licensing

[Maikoda Sutter]

If I use the kernel as a basis for my own system and modify the kernel
should I still maintain the licensing of the kernel bits, or could release
it under it's own license?

For example: I would like to rewrite the headers to be 100% POSIX compliant
and I do like the BSD license, however I was planning on releasing my whole
system under the Unlicense, I understand that certain headers and code that
I do not modify has to be released under the BSD license as that is the
original license of the code, however for headers or code that I modify can
I release it under the Unlicense (http://unlicense.org/)?

I do plan on giving credit where it is due and such to the wonderful
developers of FreeBSD and those that wrote the original code because
without you I would not be able to produce so rapidly that which I am
looking to produce I just would like clarification on the extent that I
would have to license things via the BSD license.

Respectively Yours,

Maikoda Raine
Arrogant Penguin Industries