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Two female students were allegedly followed by a man after school along Markland Road and Church Road on Wednesday.
The police say the man made no approach or attempt to speak or touch them.
It is believed the girls attended Dover’s St Martins’ School, and the area's neighbourhood watch forum has been informed.
The details of where the girls were allegedly followed changed after a police officer took a statement from them on Thursday, February 5.
Parents were in talks on social media about the incident after the school told parents by text on Wednesday evening.
The text said: “Just to inform you that two of our children have notified us that they have been followed by a white male in his 40s, dressed in black, in the vicinity of the school. The police are aware.”
A Kent Police spokesman said: "They did exactly the right thing and went back to the safety of their school to report it."
He later added: "The details have been circulated to Neighbourhood Watch and local officers and local schoolchildren get regular inputs about keeping safe from their schools."
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