Dendrimers are branched synthetic macromolecules. This protocol describes the synthesis (1-2 weeks), functional screening (1.5 d) and decoding (2 d) of 'one-bead-one-compound' combinatorial libraries of dendrimers assembled from amino-acid building blocks by 'split-and-mix' solid phase peptide synthesis. The method resembles that for synthesizing linear peptides, except that a branching diamino acid is used at every third position to obtain the dendritic structure. Structural diversification by splitting is restricted to four amino acids per variable position, yielding libraries of approximately 60,000 sequences. In such libraries, the sequence of a dendrimer can be deduced uniquely from an amino-acid analysis of the solid support bead. This analysis is more reliable, faster and far less costly than Edman sequencing such that decoding multiple beads is affordable. The method is exemplified for the identification of catalytic peptide dendrimers catalyzing the hydrolysis of acyloxypyrene-trisulfonates with substrate binding (K(M) = 10-300 microM) and rate accelerations up to k(cat)/k(uncat) = 10(4) in aqueous buffer.