Provided is a process for alleviating bleeding between a black image and a color image adjoining each other on a recording medium, both of the images being formed on the recording medium by an ink jet process, comprising the steps of: (i) applying a black ink comprising a self-dispersing anionically charged carbon black to an area where the black image is to be formed; and (ii) applying a color ink to an area where the color image is to be formed, wherein the black ink further contains at least one salt selected from the group consisting of (M1)2SO4, CH3COO(M1), Ph-COO(M1), (M1)NO3, (M1)Cl, (Ml)Br, (M1)I, (M1)2SO3 and (M1)2CO3, where M1 is an alkali metal, ammonium or organo-ammonium and Ph is a phenyl group, and wherein the color ink comprises an anionic dye.