Present invention relates to an aqueous oxidizing composition comprising at least one oxidizing agent and at least one organic solvent. It has surprisingly been found out that an aqueous oxidizing composition comprising at least one oxidizing agent and at least one organic solvent does effectively recover disulfide bonds in hair after a reducing treatment and hair permanently shaped with the said composition has excellent curling or straightening efficiency and hair dyed with the use of the said composition is homogeneously dyed and appears to look more natural and feels natural upon touching in terms of softness, smoothness, and grip.