  As a basic mechanical parameter, Poisson's ratio ({\nu}) measures the
mechanical responses of solids against external loads. In rare cases, materials
have a negative Poisson's ratio (NPR), and present an interesting auxetic
effect. That is, when a material is stretched in one direction, it will expand
in the perpendicular direction. To design modern nanoscale electromechanical
devices with special functions, two dimensional (2D) auxetic materials are
highly desirable. In this work, based on first principles calculations, we
rediscover the previously proposed {\delta}-phosphorene ({\delta}-P) nanosheets
[Jie Guan et al., Phys. Rev. Lett. 2014, 113, 046804] are good auxetic
materials with a high NPR. The results show that the Young's modulus and
Poisson's ratio of {\delta}-P are all anisotropic. The NPR value along the
grooved direction is up to -0.267, which is much higher than the recently
reported 2D auxetic materials. The auxetic effect of {\delta}-P originated from
its puckered structure is robust and insensitive to the number of layers due to
weak interlayer interactions. Moreover, {\delta}-P possesses good flexibility
because of its relatively small Young's modulus and high critical crack strain.
If {\delta}-P can be synthesized, these extraordinary properties would endow it
great potential in designing low dimensional electromechanical devices.
