  After Strassen presented the first sub-cubic matrix multiplication algorithm,
many Strassen-like algorithms are presented. Most of them with low asymptotic
cost have large hidden leading coefficient which are thus impractical. To
reduce the leading coefficient, Cenk and Hasan give a general approach reducing
the leading coefficient of $<2,2,2;7>$-algorithm to $5$ but increasing IO
complexity. In 2017, Karstadt and Schwartz also reduce the leading coefficient
of $<2,2,2;7>$-algorithm to $5$ by the Alternative Basis Matrix Multiplication
method. Meanwhile, their method reduces the IO complexity and low-order
monomials in arithmetic complexity. In 2019, Beniamini and Schwartz generalize
Alternative Basis Matrix Multiplication method reducing leading coefficient in
arithmetic complexity but increasing IO complexity. In this paper, we propose a
new matrix multiplication algorithm which reduces leading coefficient both in
arithmetic complexity and IO complexity. We apply our method to Strassen-like
algorithms improving arithmetic complexity and IO complexity (the comparison
with previous results are shown in Tables 1 and 2). Surprisingly, our IO
complexity of $<3,3,3;23>$-algorithm is $14n^{\log_323}M^{-\frac{1}{2}} +
o(n^{\log_323})$ which breaks Ballard's IO complexity low bound
($\Omega(n^{\log_323}M^{1-\frac{\log_323}{2}})$) for recursive Strassen-like
algorithms.
