  A new spin wavelet transform on the sphere is proposed to analyse the
polarisation of the cosmic microwave background (CMB), a spin $\pm 2$ signal
observed on the celestial sphere. The scalar directional scale-discretised
wavelet transform on the sphere is extended to analyse signals of arbitrary
spin. The resulting spin scale-discretised wavelet transform probes the
directional intensity of spin signals. A procedure is presented using this new
spin wavelet transform to recover E- and B-mode signals from partial-sky
observations of CMB polarisation.
