Let Λ \Lambda be an artin algebra, let mod Λ \bmod \Lambda be the category of finitely generated Λ − modules \Lambda - {\text {modules}} , and let p d 1 mod Λ p{d_1} \bmod \Lambda be the subcategory of mod Λ \bmod \Lambda consisting of the modules of projective dimension less than or equal to one. In this paper it is proved that if the projective dimension of the injective envelope of Λ \Lambda as a Λ − module \Lambda - {\text {module}} is less than or equal to one, then p d 1 mod Λ p{d_1}\bmod \Lambda is contravariantly finite in mod Λ \bmod \Lambda . It also contains an example of finitistic projective dimension one where p d 1 mod Λ p{d_1}\bmod \Lambda is not contravariantly finite in mod Λ \bmod \Lambda .