Necessary and sufficient conditions for a function to be a multiplier mapping the Besov space B-1(m)(R-n) into the Besov space B-1(l)(R-n) with integer l and m, 0 < l <= m, are found. It is shown that multipliers between B-1(m)(R-n) and B-1(l)(R-n) form the space of traces of multipliers between the Sobolev classes W-1(m+1)(R-+(n+1)) and W-1(l+1)(R-+(n+1)).