Aiming at the question whether the group generated by two unipotent matrices whose Jordan blocks are of order no more than five is a unipotent group

based on the fundamental definition of nilpotent matrix

we use the matrix logarithm tool to obtain some combinatorial properties of the generators of free groups

and then use the combinatorial properties obtained to carry out theoretical derivation

and finally prove that the group generated by the matrices whose block are of order no more than five is a unipotent group if every primitive is unipotent and their Jordan blocks are of order no more than five. We also strive to provide new ideas and methods for studying the related properties of unipotency.