With the increasing use of machine learning software in our daily life, software fairness has become a growing concern. In this paper, we propose an individual fairness testing technique called KOSEI. Individual fairness is one of the central concepts in software fairness. Testing individual fairness aims to detect individual discriminations included in the software. KOSEI is based on AEQUITAS by Udeshi et al., a landmark fairness testing technique featuring a two-step search strategy of global and local search. KOSEI improves the local search part of AEQUITAS, based on our insight to overcome the limitations of the local search of AEQUITAS. Our experiments show that KOSEI outperforms AEQUITAS by orders of magnitude. KOSEI, on average, detects 5,084.8% more discriminations than AEQUITAS, in just 7.5% of the execution time.