We predict a new class of monolayer phosphorus allotropes, namely, ε-P, ζ-P, η-P, and θ-P. Distinctly different from the monolayer α-P (black) and previously predicted β-P (Phys. Rev. Lett. 2014, 112, 176802), γ-P, and δ-P (Phys. Rev. Lett. 2014, 113, 046804) with buckled honeycomb lattice, the new allotropes are composed of P4 square or P5 pentagon units that favor tricoordination for P atoms. The new four polymorphs, together with five additional hybrid polymorphs, greatly enrich the phosphorene structures, and their stabilities are confirmed by first-principles calculations. In particular, the θ-P is shown to be equally stable as the α-P (black) and more stable than all previously reported phosphorene polymorphs. Prediction of nonvolatile ferroelastic switching and structural transformation among different polymorphs under strains points out their potential applications via strain engineering.