We have developed the uncoupled version of multireference Mukherjee's coupled cluster method with connected triexcitations. The method has been implemented in ACES II program package. The agreement between the uncoupled and the standard version of Mukherjee's multireference coupled cluster method has been reported previously at the singles and doubles level by Das et al. [J. Mol. Struct.: THEOCHEM 79, 771 (2006); Chem. Phys. 349, 115 (2008)]. The aim of this article is to investigate this method further, in order to establish how its performance changes with the size of the basis set, size of the model space, multireference character of different molecules, and inclusion of connected triple excitations. Assessment of the new method has been performed on the singlet methylene, potential energy curve of fluorine molecule, and third b (1)Σ(g)(+) electronic state of oxygen molecule.