We extend the analysis of the MAXIMA-1 cosmic microwave background data to
smaller angular scales. MAXIMA, a bolometric balloon-borne experiment, mapp
ed a 124 deg(2) region of the sky with 10' resolution at frequencies of 150
, 240, and 410 GHz during its first flight. The original analysis, which co
vered the multipole range 36 less than or equal to l less than or equal to
785 using a 100 deg(2) map, is extended to l = 1235 using a subset of the d
ata from three 150 GHz photometers in the fully cross-linked central 60 deg
(2) of the map. The main improvement over the original analysis is the use
of 3' square pixels in the calculation of the map. The new analysis is cons
istent with the original for l < 785. For l > 785, where inflationary model
s predict a third acoustic peak, the new analysis shows power with an ampli
tude of 56 +/- 7 muK at l similar or equal to 850 in excess to the average
power of 42 +/- 3 muK in the range 441 < l < 785.