  In this paper we introduce efficient algorithm for the multiplication of
split-octonions. The direct multiplication of two split-octonions requires 64
real multiplications and 56 real additions. More effective solutions still do
not exist. We show how to compute a product of the split-octonions with 28 real
multiplications and 92 real additions. During synthesis of the discussed
algorithm we use the fact that product of two split-octonions may be
represented as vector-matrix product. The matrix that participates in the
product calculating has unique structural properties that allow performing its
advantageous decomposition. Namely this decomposition leads to significant
reducing of the multiplicative complexity of split-octonions multiplication.
