FOAM QUALITY AND DISCHARGE PROPERTIES ARE IMPROVED BY USING A SQUEEZE CONTAINER TO DISCHARGE A MIXED SOLUTION (A3) OF FIRST AND SECOND AGENTS (A1,A2) OF A TWO-PART HAIR COSMETIC FOR HAIR DYEING OR BLEACHING (1) IN A FOAM. A TWO-PART HAIR COSMETIC (1) FOR HAIR DYEING OR BLEACHING INCLUDES A FIRST AGENT (A1) CONTAINING AN ALKALINE AGENT AND A SECOND AGENT (A2) CONTAINING HYDROGEN PEROXIDE AND A SQUEEZE CONTAINER (6) FOR DISCHARGING A MIXED SOLUTION (A3) OF THE FIRST AGENT (A1) AND THE SECOND AGENT (A2) THE FIRST AGENT (A1) OR SECOND AGENT (A2) CONTAINS A FOAMING AGENT. THE MIXED SOLUTION (A3) THEREOF HAS A VISCOSITY (25°C) OF FROM 1 mPa.s TO 100 mPa.s. A SQUEEZE FOAMER (5) OF THE SQUEEZE CONTAINER (6) HAS A GAS-LIQUID MIXING CHAMBER (11) FOR CAUSING THE MIXED SOLUTION TO FOAM, FOAM HOMOGENIZING MEANS (14,18) FOR HOMOGENIZING FOAM OF THE MIXED SOLUTION WHICH HAS BEEN MADE TO FOAM IN THE GAS-LIQUID MIXING CHAMBER (11), AND A DISCHARGE OUTLET (17) FOR DISCHARGING THE HOMOGENIZED FOAM. THE RATIO BETWEEN THE TOTAL VOLUME OF THE FIRST AND SECOND AGENTS (A1, A2) AND THE INNER VOLUME OF THE CONTAINER BODY IS IN THE RANGE OF FROM 0.30 TO 0.60. THE TORSO CROSS-SECTION OF THE CONTAINER BODY HAS A RATIO OF MINOR AXIS (La) TO MAJOR AXIS (Lb) OF FROM 0.5 TO 1.0, AND AN AREA OF FROM 12 CM² TO 30 CM².