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Not true. How many times a person gets to apply for H1B depends on the employer. May grad and Dec grad may get same number of chances or different. Consider this, a after graduating in Dec, assume that the student gets a new job in Feb/March, it might be too late to get all the documents together and apply by April1 deadline(Here the student has not had a job earlier and joined in Feb/March, but applied and got a job in that time period). On the other hand, if the student graduating in May get a job in Oct/Nov, then many companies do apply for H1B visa even before the student joins the company.

Also now that the STEM extension is increased to 36 months, people graduating in May may get one more shot at H1B than those graduating in Dec.

Timeline: Assuming a student graduates in May 17, Company can apply in April 17, 18,19,20. (Opt begins in June 17 and ends in June 20). Application in April 17 depends on when the student gets a job and whether the company applies before joining.

Grad graduating in Dec 16. The company can apply in April 17,18,19. Opt starts in Jan 17 and ends in Jan 20)