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Keane Wallis-Bennett died after the wall in the PE block at Liberton High collapsed on her on the 1st of April.
The school was closed after the 12 year old's death to allow checks to be carried out on the safety of the building.
The letter, which should be arriving at pupils homes today, says engineers didn't find any structural problems but work has been carried out on two ceilings in the teaching block as a precaution.
It also says psychological support, which has been available to pupils and staff since the tragedy, will continue as long as it's needed.
Keane will be laid to rest on Thursday as a service at Mortonhall crematorium.
Mourners are being asked to wear bright colours and her close friends are expected to wear oneses.
The school says as a mark of respect, and to allow any pupils to attend the funeral, the Easter revision programme has been cancelled for the day.
The school will remain open to offer any support to pupils who need it. Council bosses are thanking everyone for the overwhelming support for Keane's family and friends and pupils and staff.
Liberton High will be open on Tuesday the 22nd of April.