If a particular candidate is present in maximum four Cells in four Rows and if these Cells belong to the same Columns forming a four-by-four rectangular pattern, except for one Row where the candidate is also present in Cell(s) of this Row that belong to the same Square as one of the Cells of the four-by-four rectangular pattern (these extra-cells are called the "fin" and the related Cell in the four-by-four rectangular pattern is called the "finned" Cell), then the candidate can not be the solution for any Cell in the Column of the Square containing the "fin", except of course for the "finned" Cell.

Indeed, either the candidate is the solution for the "finned" Cell or for a Cell in the "fin" which eliminates it from all other Cells in the same Square, or it is the solution for one of the Cells in the four-by-four rectangular pattern in the same Column as the "finned" Cell, which eliminates it from all other Cells in that column.

The reasoning is also applicable when you replace "Row" by "Column" and "Column" by "Row".

The candidate must not be present in all Cells of the pattern, as long as the Cells where it is not present are "solved" Cells (i.e. either contain an initial value, or an induced value). Because of the "fin" it might even be absent from an unsolved "finned" Cell.

In the example above the Finned Jellyfish is made of Rows "B", "D", "F" and "G", and of Columns "4", "6", "8" and "9".
G9 is the "finned" Cell.
The "fin" comprises G7 only, as G8 is a clue.
If candidate 6 is the solution in D9, then it is false in all other Cells of Column "9".
If candidate 6 is not the solution in D9, then it must be true in Columns "4", "6" and "8" in Rows "B", "D" and "F", leaving only G7 and G9 available in Row "G", which eliminates all other candidates 6 in Square 9.
Hence candidate 6 can never be the solution in H8 or J8.

You can practice this strategy by installing the SudokuCoach application on your Android™ device.