  Almost all massive galaxies today are understood to contain supermassive
black holes (SMBH) at their centers. SMBHs grew by accreting material from
their surroundings, emitting X-rays as they did so. X-ray Luminosity Functions
(XLFs) of Active Galactic Nuclei (AGN) have been extensively studied in order
to understand the AGN population's cosmological properties and evolution. We
present a new fixed rest-frame method to achieve a more accurate study of the
AGN XLF evolution over cosmic time. Normally, XLFs are constructed in a fixed
observer-frame energy band, which can be problematic because it probes
different rest-frame energies at different redshifts. In the new method, we
construct XLFs in the fixed rest-frame band instead, by varying the observed
energy band with redshift. We target a rest-frame 2$-$8 keV band using
XMM-Newton and HEAO 1 X-ray data, with 7 observer-frame energy bands that vary
with redshift for $0 < z < 3$. We produce the XLFs using two techniques; one to
construct a binned XLF, and one using a Maximum Likelihood (ML) fit, which
makes use of the full unbinned source sample. We find that our ML best-fit pure
luminosity evolution (PLE) results for both methods are consistent with each
other, suggesting that performing XLF evolution studies with the high-redshift
data limited to high-luminosity AGN is not very sensitive to the choice of
fixed observer-frame or rest-frame energy band, which is consistent with our
expectation that high-luminosity AGN typically show little absorption. We have
demonstrated the viability of the new method in measuring the XLF evolution.
