The attenuation coefficient slope(ACS) is an essential property of biological tissues. Most of the present ACS estimation methods use spectrum-based approaches in B-mode imaging and need a reference phantom. A method to map ACS without a reference phantom is proposed in Synthetic Transmit Aperture ultrasound imaging. The diffraction effect in ACS estimation is studied. In this paper, the transducer bandwidth was divided into overlapping sub-bands, and each sub-band was used to reconstruct an image and yield the corresponding sub-band attenuation coefficient to obtain ACS. The feasibility of the proposed method was demonstrated in numerical simulations and experiments.