Murder Most Unladylike by Robin Stevens

At Deepdean School for Girls, Daisy Wells and Hazel Wong have set up their own detective agency. But they are struggling to find any real crimes to investigate.

(Unless you count the case of Lavinia's missing tie. Which they don't.)Then Hazel discovers the Science Mistress, Miss Bell, lying dead in the Gym. To add to the mystery, when she and Daisy return five minutes later, the body has disappeared.

Now Hazel and Daisy not only have a murder to solve: they have to prove one happened in the first place.