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The rare t-quark decays $t \to c l_j^{+} l_k^{-}$, $t \to c \tilde{\nu_j}\nu_k$ via the scalar leptoquark doublets are investigated in the minimal fourcolor symmetry model with the Higgs mechanism of the quark-lepton masssplitting. The partial widths of these decays are calculated and the totalwidth of the charged lepton mode $ \Gamma(t \to c {l^{+}}' l^{-})= \sum_{j,k}\Gamma(t \to c l_{j}^{+} l_{k}^{-})$ and the total width of the neutrino mode $\Gamma(t \to c \tilde{\nu}' \nu)= \sum_{j,k} \Gamma(t \to c \tilde{\nu_{j}}\nu_{k})$ are found. The corresponding branching ratios are shown to be $ Br(t\to c {l^{+}}' l^{-}) \approx (3.5 - 0.4) 10^{-5}, $ $ Br(t \to c{\tilde{\nu}}' \nu) \approx (7.1 - 0.8) 10^{-5} $ for the scalar leptoquarkmasses $ m_{S}= 180 - 250 GeV $ and for the appropriate values $ (\sin{\beta}\approx 0.2) $ of the mixing angle of the model. The search for such decays atLHC may be of interest.Comment: 18 pages, 2 figures, 1 table, to be published in Modern Physics  Letters A; corrected typo

RARE t-QUARK DECAYS $t\to c\,l_j^{+}l_k^{-}$, $t\to c\,\tilde\nu_j\nu_k$ IN THE MINIMAL FOUR-COLOR SYMMETRY MODEL