In this article, a new method to create an anomalous reflection in the desired direction is proposed. Two-dimensional grating surfaces consisting of four particles with the properties of a Huygens source are employed in each period. Then, this method is extended to the problem in which the grating surface is illuminated by a real source such as a horn. In this case, the designed grating surface has different periods in both directions to collimate the reflected wave and give an in-phase wavefront. Using our method, a high-efficiency reflectarray (RA) based on quaternary Huygens grating is designed. This RA is distinguished from common RAs due to its beam squint capability. This array offers more aperture efficiency and thus more gain in comparison to the leaky waves that inherently have low aperture efficiency. Therefore, our designed RA can compete with leaky wave antennas in many applications. The mentioned RA is designed to have the main beam in the direction of\documentclass[12pt]{minimal}
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				\begin{document}$$\left( {{\theta _0} = {{68}^{\circ }},{\varphi _0} = {{225}^{\circ }}} \right)$$\end{document}θ0=68∘,φ0=225∘, at the frequency of 12 GHz. The simulation results show the realized gain and SLL of this antenna are 24.8 dB and\documentclass[12pt]{minimal}
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				\begin{document}$$-15.5$$\end{document}-15.5dB, respectively. Also, by changing the frequency in the range of 12–15 GHz, the direction of the main beam varies from\documentclass[12pt]{minimal}
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				\begin{document}$$\left( {{{68}^{\circ }}, {{225}^{\circ }}} \right)$$\end{document}68∘,225∘to\documentclass[12pt]{minimal}
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				\begin{document}$$\left( {{{39}^{\circ }}, {{225}^{\circ }}} \right)$$\end{document}39∘,225∘.