Your grandmother's sister is your great aunt. (Some would say grand aunt).
Your great aunts' grandchild is your second cousin. Her great grandchild is your second cousin, once removed.
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Your grandmother's sister is your great aunt.
You grandmother's half-sister is your half-grandaunt.
Your grandmother's sister is your great aunt. You are her great niece, if you are a girl, or her great nephew, if you are a boy.
The grandchild of your great grandmother's sister is your second cousin, once removed.
Your mother's mother is your grandmother. Your grandmother's sister is your great aunt, and your mother's aunt.
Your grandmother's sister's daughter's grandson is your second cousin, once removed.
Your grandmother's sister is your great aunt. Her son's child is her grandchild. You and your great aunt's grandchild are second cousins.
Your great grandmother's sister is your great great aunt and you are her great great niece (if you are female) or great great nephew (if you are make).
Your great great grandmother's sister is your great great grandaunt, some would say great great greataunt.
Your grandmother's sisters daughter is your parent's first cousin, and your first cousin, once removed.
You are second cousins once removed.
Your grandmother's sister's grandchildren are your second cousins.