gistfile1.txt

declare
   File_Size    : Ada.Directories.File_Size := Ada.Directories.Size ("your_file");
   Record_Bytes : Integer                   := Your_Record'Size * 8;
   Num_Records  : Integer                   := File_Size / Record_Bytes;
   First        : Integer                   := Num_Records - 4

   File         : ada.streams.stream_io.file_type;
   Stream       : ada.streams.stream_io.Stream_Access;
   Values       : array (1..4) of Your_Record;
begin
   ada.streams.stream_io.open (File, in_File, "your_file");
   ada.streams.stream_io.set_Index (File, First * Record_Bytes);
   Stream := ada.streams.stream_io.stream (File);

   your_record'Read (Stream, Values (1));
   your_record'Read (Stream, Values (2));
   your_record'Read (Stream, Values (3));
   your_record'Read (Stream, Values (4));

   ada.streams.stream_io.close (File);
end;   

Why not use Ada.Direct_IO for this?