Abstract: This study is about Hyper g-matrices. Matrices are indispensable in the world of science. Many specific definitions are given on this subject. The main subject of the study is the set of cartesian products of g-matrices. The properties of matrices for these special g-matrices are included. The ordered pairs of matrices satisfying these properties are analyzed. The matrices forming this set are called hyper g-matrices. The set containing these elements is denoted by $$HG(D_{1}, D_{2})$$, where $$D_{1}, D_{2}$$ are diagonal matrices. $$HG(D_{1}, D_{2})$$ is seen to be a relation. Examples, properties, lemmas and theorems for hyper g-matrices are given.