  The class of non-commutative hypercomplex number systems (HNS) of 4-dimension
constructed by using of non-commutative procedure of Grassman-Clifford doubling
of 2-dimensional systems is investigated in the article. All HNS of this class
are constructed, algorithms of performance of operations and methods of
algebraic characteristics calculation in them, such as conjugation,
normalization, a type of zero dividers are investigated. Formulas of
exponential functions representation in these systems are displayed.
