Properties of the Cauchy--Jost (know also as Cauchy--Baker--Akhiezer) function in the case of pure solitonic solution are discussed in detail. In terms of this function action of the Ba\"acklund transformation is derived. Transformation of an auxiliary totally nonnegative matrix parameterizing generic soliton solution under such transformations is given. Relation of the Ba\"acklund transformation with property of total nonnegativity property of matrices is discussed.