Improvement of prediction accuracy of the protein secondary structure is essential for further developments of the whole field of protein research. In this paper, the expertness of protein secondary structure prediction engines has been studied in three levels and a new criterion has been introduced in the third level. This criterion could be considered as an extension of the previous ones based on amino acid index. Using this new criterion, the expertness of some high score secondary structure prediction engines has been reanalyzed and some hidden facts have been discovered. The results of this new assessment demonstrated that a noticeable harmony has been existed among each amino acid prediction behavior in all engines. This harmony has also been seen between single global propensity and prediction accuracy of amino acid types in each secondary structure class. Moreover, it is shown that Proline and Glycine amino acids have been predicted with less accuracy in alpha helices and beta strands. In addition, regardless of different approaches used in prediction engines, beta strands have been predicted with less accuracy.