  We present the first robust evidence of an anti-correlation between the X-ray
photon index, \Gamma, and the X-ray luminosity in a single low luminosity
active galactic nuclei (LLAGN), NGC 7213. Up to now, such anti-correlation
trends have been seen only in large samples of LLAGN that span a wide range of
X-ray fluxes, although the opposite behaviour (i.e. a positive correlation
between \Gamma and X-ray luminosity) has been extensively studied for
individual X-ray bright active galactic nuclei. For NGC 7213, we use the
long-term X-ray monitoring data of Rossi X-ray Timing Explorer (RXTE),
regularly obtained on average every two days from March 2006 to December 2009.
Based on our X-ray data, we derive the \Gamma versus flux and the hardness
ratio versus flux relations, indicating clearly that NGC 7213 follows a `harder
when brighter' spectral behaviour. Additionally, by analysing radio and optical
data, and combining data from the literature, we form the most complete
spectral energy distribution (SED) of the source across the electromagnetic
spectrum yielding a bolometric luminosity of 1.7*10^43 erg s^-1.
Phenomenologically, the SED of NGC 7213 is similar to that of low-ionization
nuclear emission-line region. The robust anti-correlation trend that we find
between \Gamma and X-ray luminosity together with the low accretion rate of the
source, 0.14 per cent that of Eddington limit, make NGC 7213 the first LLAGN
exhibiting a similar spectral behaviour with that of black hole X-ray binaries
in `hard state'.
