higher school—higher education beyond school, especially to degree level:
- It is hard to predict an individual’s ability to master the higher school program.
upper school—a secondary school for children aged from fourteen upwards:
- Physical education classes are part of the upper school weekly schedule.
Note: The expression does not correlate in meaning with the phrase finishing school—private school preparing upper-class girls for social life:
- She attended one term at a Swiss finishing school after which she ended her formal schooling and obtained a job.