Confirmatory Factor Analysis is an advanced statistical method used to test a pre-established hypothesis about the underlying relationships among observed variables using a limited set of factors. The primary step in the complete modeling process involves computing the correlation matrix implied by the model. Many methods are used to compute this matrix. Unfortunately, all these methods are based on the assumption that errors are uncorrelated. This assumption is not valid in reality and was introduced to facilitate the model estimation. The present paper introduces a new algorithm that overcomes these limitations. Besides, numerical simulations that show the advantages of this algorithm on the factors influencing sustainable urban livability are presented.