Improve a weak random binary sequence

I've created a Pseudo-Random Generator in Java in a completely new way (complex to explain). But sadly this generator creates weak binary random sequences. For an example the sequence 010000000100 has to many zeros.

Now I'm searching for different ways to improve created random sequences, respectively making the sequences more random, without changing the generator. My first idea is combinining runs of zeros ("0", "0000000" "00" in the example above), and runs of ones ("1", "1") to one or more binary values. Or I can determine the length of the zero runs like five/six in "0000001000001" and create a new binary random sequence with this informations like "101110". Would that be wise?

Do you know any other methods to do this?

Thanks for helping!