A contact unit for use within a connector includes a primary piece essentially composed of an upper part and a lower part coupled with each other. The upper part includes an upper retaining section and a resilient upper contacting arm with an upper contacting section and an upper abutment section at a free end thereof. The lower part includes a lower retaining section and a resilient lower contacting arm extending downwardly with a lower contacting section and a lower abutment section at a free end thereof. A secondary piece is spaced from and opposite to the primary piece in a horizontal direction of the contacting arm, and includes an upper abutment region adapted to be abutted against by the upper abutment section of the upper contacting arm, and a lower abutment region adapted to be abutted against by the lower abutment section of the lower contacting arm.