I used the structure manipulation scripts provided by [AIRSS][1] to generate the conventional cell associated with your primitive cell. I think AIRSS uses [Spglib][2] under the hood for this task, so you could probably use Spglib directly if you wanted.

__Original cell__

[![enter image description here][3]][3]

__New cell__

[![enter image description here][4]][4]

__POSCAR file__


    POSCAR
    1.0000000000000000     
    10.0886200000   0.0000000000   0.0000000000
    0.0000000000   7.1337300000   0.0000000000
    -2.5221540330   0.0000000000  10.0886187273
    A         B         
    16        48
    Direct
    0.0000000000   0.0000000000   0.0000000000
    0.4375000000   0.5000000000   0.7500000000
    0.0937500000   0.2500000000   0.8750000000
    0.0312500000   0.2500000000   0.6250000000
    0.6875000000   0.5000000000   0.7500000000
    0.0937500000   0.7500000000   0.8750000000
    0.0312500000   0.7500000000   0.6250000000
    0.5625000000   0.5000000000   0.2500000000
    0.5000000000   0.5000000000   0.0000000000
    0.9375000000   0.0000000000   0.7500000000
    0.5937500000   0.7500000000   0.8750000000
    0.5312500000   0.7500000000   0.6250000000
    0.1875000000   0.0000000000   0.7500000000
    0.5937500000   0.2500000000   0.8750000000
    0.5312500000   0.2500000000   0.6250000000
    0.0625000000   0.0000000000   0.2500000000
    0.3750000000   0.5000000000   0.5000000000
    0.2187500000   0.2500000000   0.3750000000
    0.3125000000   0.5000000000   0.2500000000
    0.1562500000   0.2500000000   0.1250000000
    0.2500000000   0.5000000000   0.0000000000
    0.1875000000   0.5000000000   0.7500000000
    0.1250000000   0.5000000000   0.5000000000
    0.2187500000   0.7500000000   0.3750000000
    0.9687500000   0.2500000000   0.3750000000
    0.0625000000   0.5000000000   0.2500000000
    0.1562500000   0.7500000000   0.1250000000
    0.9062500000   0.2500000000   0.1250000000
    0.8437500000   0.2500000000   0.8750000000
    0.9375000000   0.5000000000   0.7500000000
    0.7812500000   0.2500000000   0.6250000000
    0.8750000000   0.5000000000   0.5000000000
    0.9687500000   0.7500000000   0.3750000000
    0.8125000000   0.5000000000   0.2500000000
    0.9062500000   0.7500000000   0.1250000000
    0.7500000000   0.5000000000   0.0000000000
    0.8437500000   0.7500000000   0.8750000000
    -0.0000000000   0.5000000000   0.0000000000
    0.7812500000   0.7500000000   0.6250000000
    0.6250000000   0.5000000000   0.5000000000
    0.8750000000   0.0000000000   0.5000000000
    0.7187500000   0.7500000000   0.3750000000
    0.8125000000   0.0000000000   0.2500000000
    0.6562500000   0.7500000000   0.1250000000
    0.7500000000   0.0000000000   0.0000000000
    0.6875000000   0.0000000000   0.7500000000
    0.6250000000   0.0000000000   0.5000000000
    0.7187500000   0.2500000000   0.3750000000
    0.4687500000   0.7500000000   0.3750000000
    0.5625000000   0.0000000000   0.2500000000
    0.6562500000   0.2500000000   0.1250000000
    0.4062500000   0.7500000000   0.1250000000
    0.3437500000   0.7500000000   0.8750000000
    0.4375000000   0.0000000000   0.7500000000
    0.2812500000   0.7500000000   0.6250000000
    0.3750000000   0.0000000000   0.5000000000
    0.4687500000   0.2500000000   0.3750000000
    0.3125000000   0.0000000000   0.2500000000
    0.4062500000   0.2500000000   0.1250000000
    0.2500000000   0.0000000000   0.0000000000
    0.3437500000   0.2500000000   0.8750000000
    0.5000000000   0.0000000000   0.0000000000
    0.2812500000   0.2500000000   0.6250000000
    0.1250000000   0.0000000000   0.5000000000

I realize this isn't exactly what you wanted (e.g., the new cell vectors aren't actually orthogonal), but I am leaving it here because of the comments requesting for me to undelete the answer.

  [1]: https://www.mtg.msm.cam.ac.uk/Codes/AIRSS
  [2]: https://spglib.github.io/spglib/
  [3]: https://i.sstatic.net/AhY25.png
  [4]: https://i.sstatic.net/vrwR2.png