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We propose a derivative operator formed as a function of derivatives of theelectron coordinates. When the derivative operator is applied to the Laughlinwave function, two new wave functions in the lowest Landau level at fillingfactor 1/2 are generated. For systems of 4, 6, and 8 electrons in sphericalgeometry, it is shown that the first wave function has nearly unity overlapwith the particle-hole conjugate of the Moore-Read Pfaffian wave function,therefore together with the Moore-Read Pfaffian state forms a particle-holeconjugate pair. The second wave function has essentially perfect particle-holesymmetry itself, with a positive parity when the number of electron pairs N/2is an even integer and and a negative parity when N/2 is an odd integer. Anequivalent form suggests the first wave function forms a f-wave pairing ofcomposite fermions, and the second wave function forms a p-wave pairing. Thecorresponding Non-Abelian statistics quasiparticle wave functions are alsoproposed.

Particle-Hole Symmetry and the Fractional Quantum Hall States at 5/2 Filling Factor