A substrate surface on which either a substance to detect analyte or an analyte per se is immobilized, which surface is formed by a treatment of substrate surface with a liquid which contains uncrosslinked polymer based on polyethylene glycol chain segment, said treatment conducted either simultaneously with the immobilization of said substance or analyte or after said substance or analyte has been immobilized on said surface. The non-specific adsorption of impurity protein or the like which is co-existent in sample for assay is significantly restrained.