The structural symmetry of 43 face-on galaxy images in the R (650 nm) and J (450 nm) bands are measured to determine the usefulness of symmetry as a morphological parameter. Each galaxy image is rotated by 180 degrees and subtracted from the original to obtain a quantitative value for its structural symmetry. The symmetry numbers computed for the sample are then compared with RC3 morphological types, color, and absolute blue magnitudes. A strong correlation between color and symmetry is found, and the RC3 Hubble sequence is found to be one of increasing asymmetry. The use of symmetry as a morphological parameter, and the possible causes of the asymmetries are discussed.