There's no big secret to achieving low correlation. You just have to be different. You can be different in
- timing
- direction
- positionsize
- instruments traded
To be different in (a) timing, the new strategy would need to enter at a different time, or exit at a different time, than the benchmark you're comparing against. One classic way to achieve this is to mix systems with different average trade lengths; mix VLTTF with short term trading, for example. I bet you can think of other ways to guarantee the new strategy enters and exits at a different time than the benchmark strategy. For example, the (Long Trades Only) equity curve of a Long-and-Short system has ~ Zero correlation to the (Short Trades Only) equity curve of the same system. Why? Because they always have positions at different times. When one is "in" (Long), the other is guaranteed to be "out" (not Short). And when the other is "in" (Short), the first is guaranteed to be "out" (not Long). Obvious, and yet illuminating.
To be different in (b) direction, the new strategy would need to be Long when the benchmark was Short (or vice versa). One classic way to achieve this is to mix trading-with-the-trend strategies, and NOT-trading-with-the-trend strategies. Countertrend strategies, mean-reversion strategies, retracement strategies, "fight the tape" strategies mixed with momentum strategies. I bet you can think of other ways to guarantee the new strategy enters in a direction opposite to the direction of the benchmark strategy.
To be different in (c) positionsizing, the new strategy would need to have a Heavy positionsize when the benchmark was Light (or vice versa). You could achieve this by having a wildly different portfolio size, hence wildly different betsize-per-trade. If the benchmark strategy's portfolio contains 100 tradeables, give the low correlation strategy a portfolio of only 12 tradeables. That sort of thing. But that impinges upon:
To be different in (d) instruments traded, the new strategy would need to use a different portfolio than the benchmark; AND the instruments in portfolio N would need to move (somewhat) independently from the instruments in portfolio B.