The Wnt signalling pathway transducing the stabilization of beta-catenin is essential for metazoan embryo development and is misregulated in many diseases such as cancers. In recent years models have been proposed for the Wnt signalling pathway during the segmentation process in developing embryos. Many of these include negative feedback loops build around Axin2 regulation. In this article we propose a new negative feedback model for the Wnt pathway with Dickkopf1 (Dkk1) at its core. Dkk1 is a negative regulator of Wnt signalling. In chicken and mouse embryos there is a gradient of Wnt in the presomitic mesoderm (PSM) decreasing from the posterior to the anterior end. The formation of somites and the oscillations of Wnt target genes are controlled by this gradient. Here we incorporate a Wnt gradient and show that synchronization of neighbouring cells in the PSM is important in accordance with experimental observations.