In the numerical manifold method (NMM)

the most commonly used physical cover functions are not the best choices. Along the procedure of the formation of stiffness matrix

this paper analyses the causes of the non-diagonal entries of relatively huge absolute value in stiffness matrix

when ordinary physical cover functions are used. These extremely large entries can increase the condition number of stiffness matrix to a great extent

especially when stiff spring method is used

which is very universal and basic in the NMM. This paper suggests that well-defined local physical functions

orthogonal the better

be used instead of currently used ones related to global coordinates. This choice can help to eliminate the above-mentioned phenomenon and provide a relatively well-conditioned stiffness matrix. The suggestion is straightforward to implement

causing little changes to currently used procedure

while it affords a lot to improvement of the quality of stiffness matrix. Some examples are analyzed to test the suggested cover functions. Comparisons between the stiffness matrixes based on locally- and globally-defined cover functions show that the previous ones generate better stiffness matrix in terms of condition number.