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Polite New Year greeting used from January 1st onward. More formal than あけましておめでとう.
新年おめでとうございます。今年もよろしくお願いします。
Happy New Year. I look forward to your continued friendship this year.
新年おめでとうございます。ご家族の皆様のご健康をお祈り申し上げます。
Happy New Year. I wish good health to you and your family.