Need to re-align replication topology

This is my requirement.

I need to re-align my replication topology from

Master -> Slave
      |-> Slave1

to

Master -> Slave -> Slave1

What can be done without any data loss/data inconsistency?

Adding needed info:

Master:

mysql> select @@version; +------------+ | @@version | +------------+ | 5.6.30-log | +------------+ 1 row in set (0.00 sec)

mysql> show master status; +------------------+----------+--------------+------------------+-------------------+ | File | Position | Binlog_Do_DB | Binlog_Ignore_DB | Executed_Gtid_Set | +------------------+----------+--------------+------------------+-------------------+ | mysql-bin.000006 | 120 | | | | +------------------+----------+--------------+------------------+-------------------+ 1 row in set (0.00 sec)

Slave1: mysql> SELECT @@LOG_SLAVE_UPDATES; +---------------------+ | @@LOG_SLAVE_UPDATES | +---------------------+ | 0 | +---------------------+ 1 row in set (0.00 sec)