We searched for proton decay via
p
→
μ
+
K
0
in
0.37
 
 
Mton
⋅
years
of data collected between 1996 and 2018 from the Super-Kamiokande water Cherenkov experiment. The selection criteria were defined separately for
K
0
S
and
K
0
L
channels. No significant event excess has been observed. As a result of this analysis, which extends the previous search by an additional
0.2
 
 
Mton
⋅
years
of exposure and uses an improved event reconstruction, we set a lower limit of
3.6
×
10
33
 
 
years
on the proton lifetime.