The method and apparatus are for obtaining strong white liquor and lime mud with low residual alkali content from causticized liquor. The first filter (FWL) receives causticized liquor from causticizing vessels (CT1-CT2-CT3) and is designed as pressurized two stage disc filter with 2 separate vat parts. In the first vat part non-diluted white liquor is obtained as a filtrate from the causticized liquor. The first lime mud cake accumulated on the filter discs in the first vat part is scraped off and diluted before being fed to the second vat part. In the second vat part weak liquor is obtained as a filtrate from the re-slurried first lime mud cake. The second lime mud cake accumulated on the filter discs in the second vat part is washed before being scraped off and diluted before being fed to subsequent lime mud handling.