Macro To Find Cell Value In Column

I'm trying to write a macro to do the following:

1) Take cell A1 and copy adjacent cell B1 in new sheet.
2) Then search cell B1 to find a match in column A.
3) If there is a match, I want to copy that adjacent cell in B and into the new sheet.
4) If there is no match, then leave as is from before and move onto the cell.
5) Continue for the rest of the data.

Here is an example of what i am trying to achieve This is in the first sheet:

Column A Column B
Car Saw
Dew Jacket
Pen Key
Saw Screen
Hand Shoe
Jacket Window
Screen Sock

Now I want this in the next sheet:

Column A Column B Column C Column D
Car Saw Screen Sock
Dew Jacket Window
Pen Key
Saw Screen Sock
Hand Shoe
Jacket Window
Screen SockData 1.xlsx