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In the past years quasi-conformal mapping has been typically used to design broadband electromagnetic cloaks. However, this technique has some inherit practical limitations such as the lateral beam shift, rendering the device visible or difficult to hide a large object. In this work we circumvent these issues by using strict conformal mapping to build the first isotropic cloak. Microwave near-field measurement shows that our device (with dielectric constant larger than unity everywhere) has a very good cloaking performance and a broad frequency response. The present dielectric approach could be technically extended to the fabrication of other conformal devices at higher frequencies., Comment: 5 figures