On my paper “On sufficient condition of vector optimization” (Methods of Oper. Res. 43 (1981) 151-157) I gave sufficient conditions for local Pareto minima. Those condition among others contain a very restrictive one, namely that the intersection of the kernel of performance operator and the kernel of constraints containing only 0. The present note shows the essentiality of the above-mentioned condition. Moreover in the paper a procedure is proposed how to act in the absence of that condition. The procedure is illustrated by a numerical example.