We present high-resolution high-energy and resonant x-ray-diffraction results from La2–2xSr1+2xMn2O7 for x=0.55, 0.575, and 0.60. These compounds show superlattice reflections at wave vectors of (h±,k±,l) and (h±2,k±2,l), arising from orbital ordering with associated Jahn-Teller distortions and charge ordering, respectively. We observe a phase transition boundary between the x=0.55 and x=0.575 doping levels. Samples with x=0.55 display structural characteristics similar to those previously reported for x=0.5. Compared to this the long-range order in samples with x=0.55 and x=0.6 have a distinct change in wave-vector and correlation length. We attribute this to a new orbital bi-stripe phase, accompanied by weak, frustrated, charge ordering. The observed azimuthal dependence of the orbital order reflection supports the model proposed for this new phase.\ud \u
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