If you don't need an existing index any more, you should delete it with the DROP INDEX statement. Here is an example SQL script:

CREATE TABLE student (id NUMBER(5) PRIMARY KEY,

first_name VARCHAR(80) NOT NULL,

last_name VARCHAR(80) NOT NULL,

birth_date DATE NOT NULL,

social_number VARCHAR(80) UNIQUE NOT NULL);

Table created.

CREATE INDEX student_birth_date ON student(birth_date);

Index created.

SELECT index_name, table_name, uniqueness

FROM USER_INDEXES WHERE table_name = 'STUDENT';

INDEX_NAME   TABLE_NAME  UNIQUENES

----------------------- --------------------- ---------

SYS_C004129   STUDENT   UNIQUE

SYS_C004130   STUDENT   UNIQUE

STUDENT_BIRTH_DATE STUDENT   NONUNIQUE 

DROP INDEX STUDENT_BIRTH_DATE;

Index dropped.