To provide a method for expressing an improved vector or a cloned gene derived from a prokaryote or eukaryote, and a method for producing such a kind of vector.

This improved vector contains a promoter and operator derived from λ phage, preferably does not contain active cro gene or active N gene, has one endonuclease-recognizing site or more to clone a desired gene having about 300 bp or less from a promoter and operator, and is useful as the method using a vector upon producing various kinds of procaryotic, eucaryotic and viral polypeptide, hormone, enzyme, antigen, protein and amino acid.