Maintaining weight whilst reducing body fat percentage.

Is it actually possible for a person to reduce their body fat percentage whilst maintaining the same weight? My weight is currently 89.3 kg, my BMI is 24.2 and my body fat percentage is 15.3%. Whilst I am happy with my body weight and BMI, I would like to bring my body fat percentage down to 13%. Does this automatically mean that I need to lose more weight or can it be achieved by maintaining my existing weight and replacing fat with muscle? If it is possible which type of diet and training would be most beneficial for achieving this goal?

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