The Haze is an excess of microwave intensity emission surrounding the Galactic Centre. It is spatially correlated with the γ-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 reanalysis 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 analyse 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 GHz $\, \le \nu \le \,$ 70 GHz is a power law with spectral index βH = -2.79 ± 0.08, which is flatter than the Galactic synchrotron in the same region (βS = -2.98 ± 0.04), but steeper than that obtained from previous works (βH ~ -2.5 at 23 GHz $\, \le \, \nu \le \,$ 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 (β ~ -3.2 at 2.3 GHz ≤ ν ≤ 23 GHz), and becomes flatter above 11 GHz.