We introduce a new structural order parameter called the S vector that can be associated with each atom to describe short-range order in a solid, and use it to characterize the defects (floating bonds and dangling bonds) in amorphous silicon, based on a structural model using molecular dynamics (Dyrting et al., Europhys. Lett. 48 (1999) 403). The S vector fields have statistical characteristics that are generic for all the samples produced for amorphous silicon with our existing method. The S vector at an atomic site associated with defects typically has a large magnitude, which will decay exponentially as one moves away from the defects. The S vector has an orientation with a sense when coupled to the S vectors of neighboring atomic sites that can be described by the concept of chirality. The usefulness of this chirality associated with the defect is manifested in samples with multiple defects, where the neutrality condition for chirality is statistically obeyed. In a given sample with multiple defects, once we assign the chirality to the dangling bond, we find that all dangling bonds will have same chirality and the floating bonds will have the opposite chirality. The observation of absence of odd number of defects is explained. We also find that defects do interact in a tensorial manner. Experimental relevance of the geometric characterization of metastable states in amorphous silicon is discussed in the context of electron spin resonance and the relation of the S field with the strain field.