Cannot insert duplicate key row in object with unique index The duplicate key value SQL Server

I'm getting this error:

Cannot insert duplicate key row in object 'dbo.CLIENT' with unique index 'CLIENT_idx_A'. The duplicate key value is (338393005, 1).

When I checked, the indexes, it's created like this:

CREATE UNIQUE NONCLUSTERED INDEX [CLIENT_idx_A] ON [dbo].[CLIENT] 
(
     [SOURCE_SYSTEM_CLIENT_ID] ASC,
     [SOURCE_SYSTEM_ID] ASC
)
     WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE  = OFF,
           SORT_IN_TEMPDB = OFF, IGNORE_DUP_KEY = OFF,
           DROP_EXISTING = OFF, ONLINE = OFF,
           ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON)
ON [PRIMARY]

Actually, I want to update one value in SOURCE_SYSTEM_CLIENT_ID and my SOURCE_SYSTEM_ID is 1 for all the SOURCE_SYSTEM_CLIENT_ID that I want to update. So I think, its encountering duplicate. How can I solve this?