Can one get a second Master's degree in a related field (biochemistry, bioinformatics)?
Broadly, yes.

Previously, I worked with students on masters degree who already had other masters degree or other postgraduate qualifications.  Some even had doctorate.  Taking a second masters can be really valuable, especially if you are seeking professional development.

It would depending on the institution that you are applying to for your second masters (such as how you meet the entry requirements etc.), so you would need to check with them for advice on your specific situation.

There are two considerations you need to make, however (this is speaking from a UK context):

Funding

Some funding, especially in the UK, whether student loans, scholarships from private donors, government money and research grants will not cover someone who is taking a qualification of the equivalent level that they have already obtained.  Check this with the university you are applying for.

Visa and immigration

I am not qualified to give visa advice, however, you should know that, at least in the UK at the moment, the decision to grant you a student visa might also depend upon whether you are taking a qualification equivalent to the level of one you have already obtained.

If you're an international student and got your first masters in the UK, your chances of getting a visa to stay to do a second masters could be nil.  Speak with a visa and immigration adviser at the institution you are thinking about.