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Yes. New York State is an "employmentatwill," state. Without a contract restricting termination (such as a collective bargaining agreement) an employer has the right to discharge an employee at any time for any reason. This also protects the employee's right to resign.
Exceptions to "employmentatwill" are laws enforced by the New York State Division of Human Rights, which prohibit discrimination based upon race, creed, national origin, age, handicap, gender or marital status.
Have you been discriminated against by a potential or current employer -- as a job applicant or current employee? To best protect your legal rights you should discuss your situation with an employment lawyer. Meet with a local employment attorney sooner rather than later to protect your rights.