I blocked someone who was harassing me and she is still able to send me messages

Two or three months ago a former friend began sending me harassing instant messages, so I blocked her screenname. Today, without ever having removed her screenname from my block list, I received more instant messages from her, and this time the content of those messages was exponentially more hurtful and inappropriate. Thinking that perhaps something had gone amiss when I'd blocked her initially, I unblocked and then reblocked her screenname; moments later I received still more messages. I am not sure why this problem is happening but I need it to be resolved ASAP.