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The Hosoya index is an important topological index in graph theory, which is defined as the total number of <i>s</i>-matchings, denoted as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>(</mo><mi>G</mi><mo>,</mo><mi>s</mi><mo>)</mo></mrow></semantics></math></inline-formula>, in a graph <i>G</i>. Therefore, computing the number of <i>s</i>-matchings for various molecular structures holds significant importance. By applying the concept of symmetry, defining the <i>s</i>-matching vector of the graph with a specified edge, using the transfer matrix, and iteratively applying two recursive formulas to derive the reduction formula, we compute the number of <i>s</i>-matchings of cyclooctatetraene chains.