  In many shell model interactions, the tensor force monopole matrix elements
often retain systematic trends originating in the bare tensor force. However,
in the present work, we find that Isospin T = 0 tensor force monopole matrix
elements of \textit{p}-shell effective interaction CK(8-16) do not share these
systematic. We correct these discrepancies by modifying T = 0 tensor force
two-body matrix elements (TBMEs) of CK(8-16) by the analytically calculated
tensor force TBMEs. With some additional modification of single-particle
energies and TBMEs, the revised effective interaction is named as CKN. The
effective interaction CKN has been tested for the calculations of
\textit{p}-shell nuclei of normal parity states from various physics viewpoints
such as excitation spectra, electromagnetic moments, and electromagnetic and
\textit{G}amow-\textit{T}eller (\textit{GT}) transitions. The obtained results
are found to be satisfactory.
