Eligibility for second Masters degree, NO cpt ?

Hi,

I did my first masters in Arts (2010 - 2012), completed 12 months OPT , changed to H1b for 3 years (2013 - 2016).Due to some issues h1b extension denied. Went back to India within a week, returned on F1 visa Masters in Computer Science (2017-2018).Am I eligible to do another Masters , without taking CPT and change to H1b while on F1?

Yes, you can. But, regarding H1B transfer, if you were already counted towards cap, you can apply for COS as needed. But again, doing F1 and then immediately doing COS can raise flags, speak to an attorney and make a decision. Better thing is to stay in home country, get H1B and stamping also from home country and travel to US with work visa and right intent to work.