The Pershing II missile, the heart of the North Atlantic Treaty Organization's nuclear modernization program but a failure in its first 1,000-mile flight test in July at Cape Canaveral, Fla., is to be fired for the second time this week.

This time, however, the beleaguered missile will be shot 200 miles almost straight up and less than 100 miles down White Sands Missile Test Range, N.M., according to Pentagon officials.

The unusual test of the missile's terminal guidance system was to take place after two long-range firings down the Florida range. But in an attempt to get the weapon back on its accelerated test program, the Army is going ahead with the short White Sands shot and will not attempt the next 1,000-mile firing until January.

The sophisticated guidance of the Pershing II is based on a radar correlator that compares an image of the target put into the warhead with the actual radar image received by the missile as it plunges toward the ground.

The warhead has the ability to change direction until the two images coincide.

Although the Army had some problems with initial tests of the guidance system four years ago, officials say those problems have been solved during simulator tests.

The White Sands shot will also test the newly designed motors in the missile's first and second stages. The original ones failed and caused the missile to explode 71 seconds after launch in July.

Only a test firing at the missile's full range will provide the maximum heat stress and pressure on the new motors, and such tests are necessary before the missile can be deployed with confidence.

Despite its problems, the Pershing II remains the Soviets' major aggravation about the U.S. nuclear arms buildup.

Moscow's concern stems from the missile's planned ability to deliver a nuclear warhead on Soviet soil in less than eight minutes from bases in West Germany.

The Pershing II and planned deployment of ground-launched cruise missiles to western Europe led the Soviets to agree to talks in Geneva aimed at eliminating or reducing the number intermediate-range nuclear missiles maintained by both superpowers in Europe.

Under a NATO plan approved in December, 1979, the United States was to deploy 108 Pershings in West Germany beginning in December, 1983. That date slipped to early 1984 because Bonn insisted that the Pershings could not enter West Germany until Italy began accepting ground-launched cruise missiles. Those were not scheduled for deployment to bases in Sicily until the spring of 1984.

The NATO plan, however, required the Army to accelerate development of the Pershing II by a year. Cost of the missile has almost doubled, to $2 million apiece, under the plan.

Under the speeded-up development program, the Army reduced the planned tests from 28 to 18, then was forced to delay the first of those for six months because building the missile turned out to be more complicated than expected. The program had another drastic setback when the first test failed.

Despite these problems, the Army has been forced to order production of the weapon so it could meet the NATO deployment timetable. Until testing and modifications are complete, however, only five missiles per month will be produced rather than the eventually planned 13 per month.