Osman (aka Cannon Dancer) by Mitchell, released in 1996 in the arcade.
Welcome, Reader, to one of gaming's best-kept secrets. Strider is one of Capcom's memorable, enduring hits which still gets talked about to this day; for some reason, a proper follow-up has never surfaced. Unless you count Strider 2, which I guess you kinda should, but the game was a fairly large departure from the source material. The secret in question is that there sort of was a "proper" Strider 2 - this game, Osman, was it.
The quick story is that much of the original dev team from Capcom Strider (arcade version) split from their studio of origin and went over to the far-lower-profile Mitchell (creator of Pang/Buster Bros. and Puzzloop/Ballistic - geez what is it with all these dual names today?) There, they made this game which follows very much in style and gameplay from the cues put forth by Strider, though set in a different world with different characters. One go at the controller, however, and you will see exactly what I mean.
He's got a lot of the same moves, attack patterns, the level designs all feel quite similar. No nifty sword-wielding here, as Osman is all about the punching and kicking however, but he does it with style. Overall the game feels a lot more well-crafted than it's predecessor, with nonstop challenge, more lush graphic design, and a much less stuttery presentation (Strider always felt, to me, like it was having a hard time keeping up with itself).
For a number of reasons, this game flew below the radar, and no one ever really gave it any time in the press. That's a shame, as this game is an excellent action tour-de-force and any period gamer will eat it up. Go find it, play it, and know.