Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric

In an addendum to his seminal 1969 article J"{o}reskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix. These condition sets, formulated under factor correlation and factor covariance metrics, respectively, were claimed to be equivalent and to lead to global rotational uniqueness of the factor solution. It is shown here that the conditions for the oblique factor correlation structure need to be amended for global rotational uniqueness, and hence, that the condition sets are not equivalent in terms of unicity of the solution.