SMA WITH INSTRUCTOR AND SPI HAS NMAC WITH SMT DEPARTING AFTER FROM SAME ARPT.

Narrative

I LEFT SMO WITH A STUDENT PLT IN A SMA. WE FLEW A STANDARD DEP; WITH A R TURN TO A HDG OF 315 DEGS; WHICH TOOK US ALONG THE SHORELINE. WE STAYED ONSHORE; BECAUSE THE BASES SEEMED TO BE THICKER OFFSHORE. WE REACHED 1600- 1700 MSL WHEN MY STUDENT LOOKED TO HIS L AND POINTED. I THEN SAW A SMT FLY UNDER OUR ACFT FROM THE L TO R WING. THE TAIL APPEARED MUCH CLOSER TO US. I CONTACTED SMO TWR AND RPTED THAT A SMT HAD JUST FLOWN 20-30 FT UNDER US. I HAD TO REPEAT THIS TWICE. IN THIS AREA; MOST OF THE ATTN IS GIVEN TO FLYING THE ACFT; CLBING TO A HIGHER ALT; LOOKING FOR ARR TFC ENTERING PATTERN FROM L TO R AND ACFT COMING FROM THE VFR TCA SHORELINE RTE. I HEARD THE SMT BEING CLRED FOR TKOF; BUT NEVER THOUGHT IT WOULD BE AT OUR ALT. A TWIN ENG SHOULD BE ABLE TO CLB AT A MUCH GREATER RATE THAN A SINGLE AND THEREFORE SHOULD NOT CONFLICT WITH IT. NEITHER THE SMT NOR I WERE INFORMED BY THE TWR THAT WE WERE ON A COLLISION COURSE; WHICH LEADS ME TO BELIEVE THAT THE CTLR WASNþT WATCHING THE DEP END OF HIS RADAR SCREEN. THIS ISNþT THE FIRST TIME THAT ACFT HAVE COME CLOSE TO EACH OTHER IN THIS AREA WHEN LNDG AND DEPARTING ON RWY 21.