Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)An ultracold Fermi atomic gas at unitarity presents universal properties that in the dilute limit can be well described by a contact interaction. By employing a guiding function with correct boundary conditions and making simple modifications to the sampling procedure we are able to calculate the properties of a true contact interaction with the diffusion Monte Carlo method. The results are obtained with small variances. Our calculations for the Bertsch and contact parameters are in reasonable agreement with published experiments. The possibility of using a more faithful description of ultracold atomic gases can help uncover additional features of ultracold atomic gases. In addition, this work paves the way to perform quantum Monte Carlo calculations for other systems interacting with contact interactions, where the description using potentials with finite effective range might not be accurate.926 U.S. Department of Energy, Office of Nuclear Physics [DE-AC52-06NA25396]National Science Foundation [PHY-1404405]US DOE [DE-AC02-05CH11231]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)[PVE-087/2012]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)FAPESP [FAPESP-2014/20864-2]FAPESP [FAPESP-2010/10072-0]