  In this paper we estimate the local (z<0.22) X-ray luminosity function of
`normal' galaxies derived from the XMM-Newton Needles in the Haystack Survey.
This is an on-going project that aims to identify X-ray selected `normal'
galaxies (i.e. non-AGN dominated) in the local Universe. We are using a total
of 70 XMM-Newton fields covering an area of 11 sq. degrees which overlap with
the Sloan Digital Sky Survey Data Release-2. `Normal' galaxies are selected on
the basis of their resolved optical light profile, their low X-ray--to--optical
flux ratio (log(f_x/f_o)<-2) and soft X-ray colours. We find a total of 28
candidate `normal' galaxies to the 0.5-8 keV band flux limit of ~2x10^{-15}
cgs. Optical spectra are available for most sources in our sample (82 per
cent). These provide additional evidence that our sources are bona-fide
'normal' galaxies with X-ray emission coming from diffuse hot gas emission
and/or X-ray binaries rather than a supermassive black hole. Sixteen of our
galaxies have narrow emission lines or a late-type Spectral Energy Distribution
(SED) while the remaining 12 present only absorption lines or an early-type
SED. Combining our XMM-Newton sample with 18 local (z<0.22) galaxies from the
Chandra Deep Field North and South surveys, we construct the local X-ray
luminosity function of `normal' galaxies. This can be represented with a
Schechter form with a break at L* ~ 3x10^{41} cgs and a slope of ~1.78+/-0.12.
Using this luminosity function and assuming pure luminosity evolution of the
form
  (1+z)^{3.3} we estimate a contribution to the X-ray background from `normal'
galaxies of 10-20 per cent (0.5-8 keV). Finally, we derive, for the first time,
the luminosity functions for early and late type systems separately.
