A new coefficient for measuring agreement on bidirectional response continua, called ψ^*, is presented. ψ^* is based on Holley and Guilford's "G index of agreement," which is restricted to measuring agreement in 2 × 2 tables. ψ^* instead is designed to measure agreement in larger square contingency tables with even numbers of rows and columns. ψ^* avoids some of the shortcomings of other measures of agreement; it is, e.g., independent of scale direction.