  The Bel-Robinson tensor contains many nice mathematical properties and its
dominant energy condition is desirable for describing the positive
gravitational energy. The dominant property is a basic requirement for the
quasi-local mass, i.e., in small sphere limit. We claim that there exists
another option, a linear combination between the Bel-Robinson tensor $B$ and
tensor $S$, which contributes the same dominant property. Moreover, using the 5
Petrov types as the verification, we found that this dominant property
justification for the Bel-Robinson tensor can be simplified as examining
$B_{0000}\geq|B_{\alpha\beta{}00}|$ and $B_{0000}\geq|B_{0123}|$, instead of
$B_{0000}\geq|B_{\alpha\beta\lambda\sigma}|$ for all
$\alpha,\beta,\lambda,\sigma=0,1,2,3$.
