This paper offers an alternative framework of interpretation for the sign inventory of the Linear A script, which was used on Crete and the Aegean island in the period c. 1800-1450 B.C. (late-Middle to Late Bronze Age) to write the still undeciphered Minoan language. The approach herein proposed is called ‘combinatory’, with special reference to Linear A complex (or ‘composite’) signs. It can be noticed that complex signs follow certain combination patterns, showing that the way in which Linear A simple signs are combined together to form a complex sign is meaningful, as much as the resulting composite sign. The viability of this approach and ensuing sign classification will be explored, and some of the implications resulting from applying this classification will be evaluated. The ultimate aim is to provide an alternative and more productive way of looking at the Linear A sign repertory by improving the current sign classification system.