We improve an upper bound by Hirsch on
a deterministic algorithm for solving general CNF satisfiability problem.
With more detail analysis of Hirsch's algorithm, we give some improvements, 
by which we can prove an upper bound $\widetilde{\cal O}(1.234^m)$ w.r.t.\ the number $m$ of input clauses, 
which improves Hirsch's bound $\widetilde{\cal O}(1.239^m)$.