  We study the search for an extra scalar $S$ boson produced in association
with the $Z$ boson at the International Linear Collider (ILC). The study is
performed at center-of-mass energies of 250 GeV and 500 GeV based on the full
simulation of the International Large Detector (ILD). In order to be as
model-independent as possible, the analysis uses the recoil technique, in
particular with the $Z$ boson decaying into a pair of muons. As a result,
exclusion cross-section limits are given in terms of a scale factor $k$ with
respect to the Standard Model Higgs-strahlung process cross section. These
predicted results, covering all possible searching regions of the extra scalars
at the 250 GeV ILC and the 500 GeV ILC, can be interpreted independently of the
decay modes of the $S$ boson.
