We use data from the Tenerife 10-, 15- and 33-GHz beam-switching experiment
s along with the COBE 53- and 90-GHz data to separate the cosmic microwave
background (CMB) signal from the Galactic signal, and create two maps at hi
gh Galactic latitude. The new multi-MEM technique is used to obtain the bes
t reconstruction of the two channels. The two maps are presented, and known
features are identified within each. We find that the Galactic contributio
n to both the 15- and 33-GHz Tenerife data is small enough to be ignored wh
en compared with the errors in the data and the magnitude of the CMB signal
.