The FOPI Collaboration at the GSI SIS-18 synchrotron measured charged kaons from central and semi-central collisions of Ni+Ni at a beam energy of 1.91A GeV. We present the distribution of the K$^-$K$^+$ ratio on the energy vs polar angle plane in the nucleon-nucleon center-of-mass frame, with and without subtraction of the contribution of $phi$(1020) meson decays to the K$^-$ yield. The acceptance of the current experiment is substantially wider compared to the previous measurement of the same colliding system. The ratio of K$^-$ to K$^+$ energy spectra is expected to be sensitive to the in-medium modifications of basic kaon properties like mass. Recent results obtained by the HADES Collaboration at 1.23A and 1.76A GeV indicate that after inclusion of the $phi$ meson decay contribution to the K$^-$ production no difference between the slopes of the K$^-$ and K$^+$ energy spectra is observed within uncertainties. For our data a linear fit to this ratio obtained after subtraction of the $phi$ meson contribution still shows a decrease with kinetic energy, although a constant value cannot be rejected. The contribution of $Lambda(1520) rightarrow ptext{K}^-$ decays estimated from fitting the thermal model to the experimental yields appears to be another factor of moderate relevance.
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