Update data in one table with data from another table

Need to switch 2 columns that were wrongfully imported:

Step1
Create a copy of the table - CREATE TABLE [dbo].[Client2](....

Step2
Inserted the data to the copied table -
INSERT INTO [dbo].[Client2]

           ([UniqueClientID]

     ,[Latitude]

           ,[Longitude]

           ,[ClientName])

     SELECT [UniqueClientID]

      ,[Latitude]

      ,[Longitude]

      ,[ClientName]

     FROM [dbo].[Client]

Step3
Switch the 2 column data by updating
UPDATE [dbo].[Client]

   set [Latitude] = [dbo].[Client2].[Longitude]

      ,[Longitude] = [dbo].[Client2].[Latitude]

 From [dbo].[Client],[dbo].[Client2]

 where [dbo].[Client].[UniqueClientID] = [dbo].[Client2].[UniqueClientID]

GO