  We present an efficient algorithm to multiply two hyperbolic octonions. The
direct multiplication of two hyperbolic 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 hyperbolic octonions with 26
real multiplications and 92 real additions. During synthesis of the discussed
algorithm we use the fact that product of two hyperbolic octonions may be
represented as a matrix - vector product. The matrix multiplicand that
participates in the product calculating has unique structural properties that
allow performing its advantageous factorization. Namely this factorization
leads to significant reducing of the computational complexity of hyperbolic
octonions multiplication.
