Lossless join decomposition is a way of taking a big table (called a relation) and breaking it down into smaller tables that still contain all the information from the big table. To make sure that the process is "lossless," we have to make sure that none of the information from the big table is lost when it is broken down into the smaller tables. That way, no matter how many times we break the relation down, we always get back the exact same information that we put in.