Piper Navajo pilot reported a near mid air collision with a Maule aircraft at an uncontrolled airport. The Piper Navajo pilot took evasive action to avoid a collision.

Narrative

At approximately XA55 UTC on Day 0; a near mid-air collision occurred in the proximity of 1 mile southwest of the approach end of Runway XX at ZZZ. The aircraft involved included a Piper Navajo and a Maule M7. The pilot of the Navajo announced on unicom approaching the airport; and reported crossing the field to observe the windsock and their intentions to enter left downwind and land. The ASOS at ZZZ was down and not reporting wind so the pilot of the Navajo announced their intention to overfly the field and observe the wind sock. Immediately following the Navajo pilot reporting their intention to overfly the field to check the wind; the pilot of the Maule M7 reported 10 West of ZZZ on unicom. The Navajo pilot reported this observation of the wind sock over the airport as favoring a landing on Runway XX and the intention to enter the left downwind for Runway XX. In direct communications between the pilots over unicom the Maule pilot announced their intention to follow the Navajo.The Navajo reported position on left crosswind; turning left downwind; and position on left downwind. After the Navajos position report of left downwind for XX the Maule pilot reported they were 'on a 45 to enter the left downwind' for the same runway. If Maule's report was correct; it would have placed them northwest of the runway behind the faster Navajo. It would be discovered that contrary to their report; the Maule actually made a right-hand turn into left traffic from the southwest. Seconds after the Maule reported on a 45 to the downwind; as the Navajo was about to turn left base the Maule was observed on a converging flight path from the southwest; crossing into the path of the Navajo within a few hundred feet of closure; approximately 100 ft. higher and descending. The Navajo pilot took immediate evasive action to avoid colliding with the Maule as the Maule was observed entering the pattern improperly; descending in a right turn into left base; and failing to yield.The Navajo announced the observed conflict and evasive action; after which the Maule pilot offered to yield after the conflict had been resolved by the Navajo turning away from the pattern and exiting to the West. The Navajo cleared the pattern to the West and re-entered the left downwind on a proper 45 entry and landed without further incident. After the incident the Maule's subsequent radio announcements did not include the aircraft registration number but used a call sign of simply 'Maule'. After the Navajo landed the Maule took off and departed the airport. After the incident the Navajo took off; completed one more landing and take-off at ZZZ; and then returned to ZZZ1. No physical damage or injuries resulted. What caused the issue is the pilot of the Maule not having positional awareness of their location. Following FAA prescribed procedures at uncontrolled airports to include recommended reporting locations and standard pattern entry could have prevented this near miss.