An antecedent of a JPEG image is any pixel-valued image that gets compressed to this JPEG image. This paper presents a novel robust JPEG steganography method based on a JPEG antecedent search of a given stego image. This method can be used whenever Alice is able to upload on an online platform a pixel-valued stego image and when the platform compresses the image. Since the antecedent search can be in some cases rather long for specific JPEG blocks, we heuristically restrict the number of search steps per block to a given threshold. Nevertheless, we show that even with this limitation, we can achieve errorless robustness against JPEG compression for payloads as big as 0.5 bpnzac for various quality factors. Not only can we ensure errorless robustness for uncompressed and compressed images, but we also show that the proposed robustness update of a given steganographic algorithm increases its undetectability. We then verify that this security improvement comes from preventing embedding changes in DCT blocks with saturated pixels. Finally, we demonstrate that the proposed method outperforms previous state-of-the-art robust steganography in terms of security with feature-based and deep-learning detectors.