We describe a new UV-Vis absorption setup designed to measure with improved sensitivity the absorption spectra of size-selected small metal clusters embedded in rare gas matrices. We aim at studying the electronic structure of clusters of different materials and their interaction with the matrix. The design, construction and performance of the setup is discussed and demonstrated on the absorption spectrum of Ag1 in argon. The absorption spectra for the two least abundant silver cluster ions produced by our cluster source in the size range of 1-39 atoms/cluster, namely Ag6 and Ag10 are reported. A sensitivity increase of about 20 is demonstrated.