Aims. In white-light coronagraph images, cool prominence material is sometimes observed as bright patches in the core of coronal mass ejections (CMEs). If, as generally assumed, this emission is caused by Thomson-scattered light from the solar surface, it should be strongly polarised tangentially to the solar limb. However, the observations of a CME made with the SECCHI/STEREO coronagraphs on 31 August 2007 show that the emission from these bright core patches is exceptionally low polarised. Methods. We used the polarisation ratio method of Moran & Davila (2004) to localise the barycentre of the CME cloud. By analysing the data from both STEREO spacecraft we could resolve the plane-of-the-sky ambiguity this method usually suffers from. Stereoscopic triangulation was used to independently localise the low-polarisation patch relative to the cloud. Results. We demonstrated for the first time that the bright core material is located close to the centre of the CME cloud. We show that the major part of the CME core emission, more than 85% in our case, is Hα radiation and only a small fraction is Thomson-scattered light. Recent calculations also imply that the plasma density in the patch is 8 × 10 8 cm −3 or more compared to 2.6 × 10 6 cm −3 for the Thomson-scattering CME environment surrounding the core material.