  The Haze is an excess of microwave intensity emission surrounding the
Galactic centre. It is spatially correlated with the $\gamma$-ray Fermi
bubbles, and with the S-PASS radio polarization plumes, suggesting a possible
common provenance. The models proposed to explain the origin of the Haze,
including energetic events at the Galactic centre and dark matter decay in the
Galactic halo, do not yet provide a clear physical interpretation. In this
paper we present a re-analysis of the Haze including new observations from the
Multi-Frequency Instrument (MFI) of the Q-U-I JOint TEnerife (QUIJOTE)
experiment, at 11 and 13 GHz. We analyze the Haze in intensity and
polarization, characterizing its spectrum. We detect an excess of diffuse
intensity signal ascribed to the Haze. The spectrum at frequencies
11$\,\leq\nu\leq\,$70 GHz is a power-law with spectral index $\beta^{\rm
H}=-2.79\pm0.08$, which is flatter than the Galactic synchrotron in the same
region ($\beta^{\rm S}=-2.98\pm0.04$), but steeper than that obtained from
previous works ($\beta^{\rm H}\sim-2.5$ at 23$\,\leq\,\nu\leq\,$70 GHz). We
also observe an excess of polarized signal in the QUIJOTE-MFI maps in the Haze
area. This is a first hint detection of polarized Haze, or a consequence of
curvature of the synchrotron spectrum in that area. Finally, we show that the
spectrum of polarized structures associated with Galactic centre activity is
steep at low frequencies ($\beta \sim -3.2$ at 2.3 $\leq\nu\leq$ 23 GHz), and
becomes flatter above 11 GHz.
