Hii,

Yes, you can transfer to a different city for your HSC Board Improvement Exam.  You need to follow a few steps.

Contact the new school in Buldhana to see whether they accept kids for improvement tests.
Request that your current school transfer your records to the new school.
Apply for the improvement exam through your new school.
Make sure you verify the deadlines and necessary paperwork.

It is best to contact with both institutions about the particular procedure.